You might be able to make it work if you spelled the nickname Evvy? Though some people might think it's Ewy if you do.
If I saw it spelled Evi I would think it was E-vee or else E-vi (long e long i)
I would pronounce it E-vee.
I'd pronounce it e-vee. But you could spell it Evi if you thought it would help
Eve, not Eh vee. Sorry. (Yes, people who see it written will pronounce it wrong her whole life.)
It's like Esme, a name I've always liked because I thought it was pronounced Es mee. But it's pronounced Es may. Bummer!
They would pronounce the nickname probably E-vee. You could always call her for short Lynn if you don't want someone to call her a name that sounds like Eve.