I don't plan to play FFXIV, but if I did, I might choose:
Tiger Lily
Liela Jade
Snow Flower
White Magnolia
Winter Lily
Liela Faline
Liela Snow
Well, none of those sound quite right :/ but oh well. I'd want something that had either Lily, Liela or Magnolia in it, and since my favorite color is green and my favorite season is autumn/winter, those would be cool to add.
Faline is a pretty name (fay-leen), but since it means feline-ish, it would be a bit excessive for a Mithra. Obviously if you are mithra, you are already feline-ish. You don't need it in a name to point that out. I was born in the year of the Tiger, so something mentioning tigers would be cool too I suppose.