I really like Verity Claire  Looking at your full name list, Verity Beatrix would also be nice.

Some other options I think could work--Verity Alice, Verity Jane, Verity Cora, Verity Luna, Verity Hazel & Verity Josephine.

Verity Claire is nice but if you wanted something a little more unusual in the middle spot ala Arthur Blaise (which is fab), how about:

Verity Beatrix

Verity Carys

Verity Genevieve

Verity Susannah

Verity Sage

Verity Lucia

Verity Nell

Verity Ondine

Verity Bess

Honestly, with your last name and Verity as a first most names sound good in the middle spot. I personally prefer middle names that don't end in an 'ee' sound but pretty much anything else seems like fair game. 

Does anything appeal to you?

I like Verity Beatrix G----s.  Verity is a wonderful name.

I like Verity Claire but think there's some better options, I like a number of the suggestions, especially Cora, Hazel and Josephine.  Some other -a names are appealing to me:
Verity Nora

Verity Calla 

Verity Ava

Verity Beulah

Verity Rosa

Although now I'm thinking about your last name, if it starts with a G like Givens, I think I would not use an A middle name to avoid the initials VAG!

Hi Penny,

Personally, I'd try to mix up the vowel sounds a bit more.  Verity Claire has, at least in my accent, a repeated "air" sound in the first syllable (only syllable in Claire).

I like two syllable middle names with V3rity G1v3ns.

How about Helene instead of Helena? In my opinion, it sounds better, because of the softer vowel sound and the two syllables. But then it shares the -en sound with your last name. I can't decide if that's a nice echo or a bit much.

hmmm....

Here's a thought...

what about Verity Blaise? 

Yes, Blaise is a boy's name, but "Verity Blaise" sounds pretty awesome to me.

Verity Blair Givens

 or Verity Helena Givens

 Verity Odette Givens