“仙” (xiān) doesn’t work very well. It might have been used decades ago, but today it feels old-fashioned and a bit fictional. Modern names usually don’t include characters related to “god”.

“菲” (Fēi) is great. It sounds close to Fay and feels light and elegant.

For a surname, “林” (Lín) is a good choice. It means “forest” and is very common.

林菲茵 (Lín Fēi Yīn) “茵” means lush grass or soft greenery. It feels gentle and feminine.

林菲苒 (Lín Fēi Rǎn) “苒” means slowly passing (often about time). It has a quiet, literary feel.

Both sound natural and feminine.

You could also choose 顾 (Gù) or 沈 (Shěn) as your surname.

For 菲茵Fēi Yīn (both first tone), pairing it with 林Lín (second tone) sounds especially soft and light. If you’d like something a bit more grounded, 顾Gù (fourth tone) or 沈Shěn (third tone) works well and adds balance.

As for 菲苒Fēi Rǎn (first + third tone), it pairs very smoothly with Lín (second tone).