what if a filly, mere or gelded?
Traditional
Sable
Majestic
Riverwind
Shadowfax
Aurora
Wintershade
Thundersprite
Use donkeyhorse syndrome to your advantage-- and teach vocabulary while you're at it!
Here's a quick random unicorn name generator, though it seems to skew male. Maybe swap out "beard" for "locks" for the lady unicorns.
Code:Roll 1d8 four times: d8 (1st) (2nd) "THE" (3rd) (4th) 1 Silver hoof Dark breaker 2 Wind beard Fiend slasher 3 Moon mane Fear slayer 4 Gold withers Sorrow ender 5 White horn Woe sunderer 6 Light leg Ruin crusher 7 Storm song Terror piercer 8 Star charger Night render