Middle Names to go with "Felicity"

I am obsessed with the name Felicity! It pairs perfectly with our last name - which begins with a P. My mother's side of the family has a tradition that girls are named with some form of "Anne" in their name. Anne, Annette, Anna etc. Unfortunately, I have realized Felicity Anne would give the initials of FAP. I feel like that is awful to saddle a little girl with. Nobody would let her live it down once she got into middle/high school. Am I being overly worried about this one, or is it valid?

Does anyone have suggestions for a way around this?

I really like the way Felicity Jean sounds (my Husbands grandmother's name), but this breaks tradition!