Meh. If someone is too dim to pronounce something phonetically, it doesn't really matter in the big scheme of things, I suppose.
DD has several friends (and a couple of teachers) who insist on calling her Ez-may, despite having been corrected on many occasions. She just sucks it up now.
If you pronounce Renée as Renny, you're an idiot (or ignorant). If you pronounce Esme (no accent) as Ez-may, same applies!
Anyway, I'm allowing myself to be sidetracked. Go for Esme, OP. It's lovely :o