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Yes, that kind of detail really helps ground a character. Names that don't seem to make any sense for a character's family situation will jolt me right out of a story. The worst I ever saw was a poor French girl, born and raised in Paris, named Skylar. No explanation. I couldn't even read the whole thing, because every time her name came up I shuddered.
To be fair, Yuna said that the character might use a name that she picked out herself rather than her birth name, which really opens up the naming options--anything that currently seems cool and appropriate would work.
Connecting it in some way to a birth name that makes sense for the character's age and family background would be great, though: a nickname that works, or maybe some etymological connection, or a similar sound or first initial. Alternatively, maybe it's a name that just CANNOT be made to work or that somehow has bad associations, so she picks something completely new and unrelated. I've seen both approaches in real life for people who are changing their name for various reasons.
I really like Beatriz for this. It's familiar enough and easy to pronounce*, but still definitely looks Spanish. I like Violeta, too, but for some reason it doesn't feel as Spanish to me, more generically "Romance".
* Easy to pronounce in my head; I have no idea whether that pronunciation is authentic...nope, according to Behind the Name that Z is pronounced -th in Spanish Spanish, so I was way off.
For an Emilia association specifically, I can recommend the old Bruce Campbell TV series "Jack of All Trades". It's probably available on NetFlix etc. (it looks like the pilot is on YouTube). It's a super-campy historical spy show, set during the Napoleonic wars. "Jack" is a swashbuckling super-spy, and Lady Emilia is his British counterpart. Think Emma Peele, but in bodice-ripping fashions :). It's very goofy, but fun, and definitely a good association for the name (at least for me).
Emilia is also a Shakespearean name, for several supporting characters. Unfortunately, two aren't very memorable and the third is somewhat of a mixed association (Iago's wife in Othello).
For context: http://www.babynamewizard.com/forum/name-remorse-help-avaoliviaevelyn?page=1
Since you mention classical gods/goddesses, maybe you'd be interested in Janus? Per Wikipedia, he was the Roman god of "beginnings, gates, transitions, time, duality, doorways, passages, and endings". You might know of him as the two-faced (as in forward-facing and backward-facing, not as in lying) god.
This seems like it would be appropriate both because of the duality of the god's nature but also because the name Janus, while male, is a homophone of the female name Janice. If your character had some connection to that name (maybe a grandmother?) it would be a really obvious choice.
I like them all, so I don't know how much help I can be. I somewhat prefer the nicknames for Elizabeth—my favorites are Eliza and Lizzie and some of the really girly ones for little girls, like Lizzibell. I also love *Pride and Prejudice*, so I have a special soft spot for the name that way. On the other hand, I slightly prefer the sound of the full name Catherine/Katherine.
For spelling, I agree that if you like Catherine best, you should use that. I actually think you might get fewer spelling issues with it; Catherine-with-a-C will almost always be heard as Catherine, but Katherine-with-a-K could equally be Kathryn or Katharine etc.
I strongly associate it with a down-at-heels town, so it's hard for me to picture as the name of an adorable baby. I imagine I could get over that once I knew said adorable baby, though.
I don't think Evelyn and Ava are too similar. However, I do think Av and Ev are too similar--actually, any combination of Ava/Av/Avie and Ev/Eve/Eva/Evie/Evva/Evvie seem too close for siblings. Ordinarily that wouldn't be a problem; I'd just say use the full name, or a nickname like Lynn. Even if other people used a truncation, it generally wouldn't be at a time when her sister was present, so it wouldn't be a problem (and if it bothered *her* to be called something so similar to her sister's name, she could just tell her friends to knock it off). But it sounds like Ev is really the nickname you like best and what you really want to use, which makes the name much more problematic as a sister to Ava.
Some other random thoughts:
I think Liv is much more usable with Ava or Av; names like Evie and Ava depend almost entirely on that very strong V for their sound, and in different situations/accents can sound almost identical. Adding another consonant into the mix really breaks up that problem. So I think Olivia would work well for you. If you want to get away from the vowel initials and really want the nickname to come straight from the front of the name, you could also consider Livia, which is a name in its own right.
If Emily seems too plain, how about Emilia? It was #102 in the US in 2016 and Amelia-with-an-A was #11, so it's more common than you may think, and you can still use the nickname Em.
Any interest in Benji? I know some folks probably still associate it with the dog, but I think it's super cute for Benjamin, and less common than plain Ben.
I have a nephew Henry; my SIL thought it would be nickname-proof, but he does indeed get called Hen. It works for him, despite any chicken associations (he's only six, though, so I can't speak for the difficult tween years). Once you've attached a word to a person, I think it gets slotted into a different category in the brain, which is why we don't automatically think of microphones for Mikes or butter for Pats.
A few ideas that lend themselves to the kind of nickname you prefer (all from the top 200 in the US in 2016, in reverse order of popularity--those closest to 200 first; sorry for any repeats!):
Girls: Juliette (Jule/Jewel), Vanessa (Van), Juliana (same as Juliette), Jocelyn (Joss), Liliana (Lil), Valentina (Val), Lydia (Lyd or Lydie), Victoria (Vic)
Boys: Waylon (Way; Wayland is the traditional spelling, but Waylon is the one climbing the charts at the moment--you'd probably need to be OK with Waylon Jenning's music to use this one, but I think the nickname Way is kind of cool), Elliott (El or Eli; I know this one was suggested for a girl, but I like it better for a boy--I also like this spelling, but combined with others it would be much higher on the list, popularity-wise), Rowan (Ro), Oscar (Oz), Calvin (Cal), Wesley (Wes or West, if you're OK with sticking in an extra letter...or using the less common spelling Westley, which was used in The Princess Bride), Miles (Mi/My), Asher (Ash)
That's going to depend partly on where the OP is, and what kind of names the folks around her like. In Rhode Island, where the "Defining girls' names" are apparently Aria, Juliana, Violet, and Mila, she might well get that reaction a lot. But in places where there's a preference for names like Riley and Aubrey (Delaware) or Ansley, Skylar, Londyn, and Taylor (Georgia) you might get just the opposite reaction: polite smiles for Arabella, and effusive praise for Auden.
Reactions before the baby is born are probably the best guide for this; just double the strength of any positive remark, and cut any negative reaction down to about one-tenth-strength, and you've probably got a pretty good proxy for what the post-birth reactions will look like.
There is an SF author named Elizabeth Moon; I really love some of her works, so that's a positive association for me. It's a pretty obscure association (it's not like naming your kid Isaac Asimov or Robin Hobb) but you might want to check out her works if you are seriously considering that name.
I generally prefer Katherine to Catherine, but both are lovely.
I agree that Diana Moon is a bit too on-the-nose. Any interest in Diantha? Similar sound, but totally different derivation.
The juxtaposition of a Catherine-with-a-C or Katherine-with-a-K issue and the name Diana makes me think of Anne of Green Gables, which makes me also want to suggest Cordelia or Anne for you :).
Good luck--I think you'll land on a lovely name, whatever you choose.
I've done it every-which-way, it seems like.
• And for our most recent, we again had a list a mile long; we actually had an official policy of putting every name suggested by a family member (even extended family) on an official list. However, I had a couple of favorites from the beginning, and the sentimental honor name that was the front-runner is what we eventually chose (but middle names weren't nailed down until after the birth, again).
One thing we didn't do was announce an official name at any time before the birth. We didn't even use the names that were decided until after the babies were born, for superstitious reasons (the twins had in utero nicknames, and the other two were pretty much just "the baby"). I was pretty open with my mother about the whole naming process, but otherwise pretty vague.
They are very different, but I think the sibling-envy would depend on personality—and could easily go the other way : "my sister got a sleek, unisex name, and I'm stuck with the girliest name on the planet!" (To be clear, that's just a hypothetical, not what I think most people would think, and of course they could each love their own name.)
I think I would look for some personal hook to give you a stronger feeling of connection to your prospective names (and a better story for your second daughter about how you picked her name). It doesn't have to be family names, it could be a hobby you both love or a place with special significance or some non-family member you admire.
The name also doesn't need to be a direct honor--for example, maybe you'd like to honor your grandfathers by picking something like one's birth month and a feminization of the other's middle name.
It may even be that some of your names already have such a connection, if you think about it. Do any beloved family members have hazel eyes, for example? Rose is the birth flower for June--maybe you were married that month, or have a beloved family member born that month. And so forth.
My strongest association is also the car, but I don't think that would necessarily be a problem in the UK. I like it in the abstract, for most of the reasons EVie mentions, but it does still sound very...corporate...or product-y, maybe...to me. A quick Google turns up several uses of the name, including religious websites and initiatives, tech companies and products, some apartments, and a video game character. Nothing that's a huge red-flag, just things to be aware of.
Maybe you would like some of the less-obvious nature-inspired names.
Names from other languages than English might work; for example, for Ocean you could use something like Kai (one of its many derivations is from Hawaiian for ocean, and it has water-related derivations in several other languages, as well), Nerissa (coined by Shakespeare, possibly from the Greek word for sea nymphs), or Naia (from Basque "wave, sea foam" and also very similar to the term naiad for water nymphs). There are also many names derived from various animal names; Ari, for example, derives independently from Hebrew for lion or German for eagle. Bernard, Dov, Humphrey, Orson, and Ursula are a few of the names that Behind the Name lists as deriving from "bear".
Trees and flowers that are less familiar, or their even less familiar scientific names, might work as well; Rowan Fence sounds much less like a punchline than Cedar Fence, for example, and I don't think something like Daphne, Linnaea, or Marguerite would even register with most people as a noun. A favorite scientific name of mine is Acer, the maple genus.
You could also look at other interests the two of you share, which might lend themselves to more name-y connections. For example, are there historical or literary figures you admire? Maybe favorite characters from books, TV, movies, video games, etc.? If you have categories you'd like to explore, folks here could probably chime in with lots of suggestions.
Or if you want names based more on flow and sound, could you give us some more examples of names that you like the sound of? Absent any other context, I'd probably lean towards longer, well-established names to balance the short-nouniness of the surname. Something that isn't generally a surname, so the full name doesn't sound like a fence company.
As others have said, you might want to look first at names you love without regard to how they "match". You might run across a name that fits this way, or you might find a name you love and realize that it makes another pattern entirely, like all have Germanic roots or all are names of Olympic medalists.
(FWIW, the way I say your children's names Amelia is closer to 4 syllables and Everett closer to 2, so I never would have noticed that pattern at all. If anything, I might look for a 1.5 syllable name, to carry on the countdown—something like Graham or Lourdes. Of course, that doesn't work very well if you're planning on having more children!)
Are you intentionally going for a Hollywood glamour vibe? Ava and Lauren together put me in mind of Ava Gardner and Lauren Bacall (quick aside: If you google the two together, you will find a lot of articles saying that they hated each other, apparently because of Frank Sinatra). If that's intentional, Olivia and Reese double down on this theme.
Otherwise, I do think personal significance would be a better tie-breaker than "flow" which is very subjective.
So is Laura the same as Lara as in Lara Croft, or is it a different vowel? That is, for me there are two ways of saying Lara, just like with Cara; in one the first vowel is like in car, and in the other more like care. I'm wondering if Laura matches one of these two for you, or if there's a third pronunciation (for me, Laura is a third--the first syllable rhymes with core).
Pretty sure non-mods can't do that.
To be fair, there really has been a reduction in spam since the latest filters were put in place.
I don't think this is thanks to requiring "and so forth"* and "human reproducti(on/ive organs)" in place of "etc" and "sex", but something they did has dropped the typical number of spam messages from dozens or hundreds each week to a handful.
* I must say, I do quite like the ring of Grandsoforthhen and Flandsoforther.