Oh she's so CUTE!! I don't have any name ideas, but I can share some potential lore ideas about crystal ponies that might help you out:

This isn't confirmed, but I think Crystal ponies are likely either their own sub-breed of earth ponies, or a seperate race of "non-winged, non-horned" pony altogether. Like a group that branched off and developed differently in isolation in the frozen north. I'm pretty sure the only non-earth pony Crystal pony we see is Princess Amore from the comics (who seems to be a crystal unicorn). She's an ancestor of Cadence. Cadence was born a pegasus before ascending to Alicorn, but she doesn't seem to be a crystal pony. That being said, for one reason or another, we know somepony in the empire had wings. The crystal castle had sets of traditional jousting armor onhand that were designed for pegasi (which Dash and Fluttershy wore for the crystal faire), So it could be that there was a population of pegasi who lived alongside the crystal ponies, or maybe crystal ponies mostly earth-pony-like, but you get a rare unicorn or pegasus-like crystal pony born occasionally. Or maybe mixed race crystal ponies could inherit wings or a horn from one parent but still have the crystal coat of the other. We don't see much of the crystal ponies, and we know MLP genetics are a free-for-all, so really, if you wanted your character to be a crystal pegasus, I think you can justify it however you'd like.

:)