To be brutally honest:
Never mind the "fag" part, but do you really want to name your child after a sleazy villain who ends up hanged, and who has an antisemitic connotation? And don't pull the excuse of "not everyone will be aware of it" because it's a really well-known character, in between the book, the musical and the various film adaptations.
If you REALLY want it it might be marginally better if you change the spelling, but not very much if it's still pronounced Fagin.
ETA: I'd suggest you look up the actual Dickens character, rather than the Disney cartoon adaptation which is bound to take away the nastier elements.
http://en.wikipedia.org/wiki/FaginThis message was edited 3/1/2009, 10:22 AM