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The name sounds very pretty - good choice. I don't see how it makes any sense at all to spell it Eva as nobody will pronounce that Ava - and legitimately so. With the accent could work. And if exotic is what you are going for, it certainly is more exotic than Ava. And if you are naming her after someone else who also spelled it that way, then by all means use the accent.

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All that said, I don't think that the alternative spellings will really set her apart from other Ava's as the pronunciation is the same and do you really want her to be "Eva with an E" as a distinction? But you seem to be aware that you are choosing a very popular name, so as long as you are okay with that.