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I wouldn't blink at a name with an accent in it (I'll probably use one myself), but if I lived in an area where nobody understands what accents do, I'd go with Ava because accent misuse is hugely irritating/ borderline infuriating to me. I think people will have a hard time knowing Eva is "eh-va" and not "ee-va" if you live in an English-only area.
I don't think accents make a name charming (or not), imo, accents are not not decorations (I'm not saying you think they are, I'm just in a touchy language mood right now and there are a lot of people who think that accents don't have a function, that they're all the same, and that one can add them in anywhere you want *grumble*). And I do think Éva is quite pretty, but I'd stay far away from accents in an English-only area because I'd be waiting for the day when someone spells it Êva or Èva or Evá or something because they know there's an accent somewhere.