The name stands alone
Here's a little pet peeve of mine: nothing rhymes with orange. You've heard that before, right? Orange is famous for its rhymelessness. There's even a comic strip called "Rhymes with Orange." Fine then, let me ask you something. What the heck rhymes with purple?
If you stop and think about it, you'll find that English is jam-packed with rhymeless common words. What rhymes with empty, or olive, or silver, or circle? You can even find plenty of one-syllable words like wolf, bulb, and beige. Yet orange somehow became notorious for its rhymelessness, with the curious result that people now assume its status is unique.
In the realm of baby names, rhymeless examples are even easier to find -- and rhyming has a more practical significance. Compare the names Kayden and Faith. Faith is far more common, but Kayden is one of 40 names rhyming with Aidan that make the boys' top-1000 list. Even a rare name like Grayden hardly sounds distinctive in a Jayden-meet-Brayden world. Faith is a top-100 name, but its stand-alone sound helps keep it from sounding overused.
I've scoured the top 200 boys' and girls' lists for fashionable names with no rhymes, near rhymes, or shared roots/nicknames in the top 1000. (A single alternate spelling can pass.) I've also ruled out all boys' names ending in -n, for reason of outrageous abundance. The names on this list may not be rare in themselves, but like orange...er, purple...they stand alone.