I would like it pronounced [name]Ah[/name]-vee-ah-na. Is that how you would say it?
yes that is how i would say it
I say it Ay-vee-ah-nuh
I say it [name]Ah[/name]-vee-ah-na, too.
I say ay-vee-ah-nah, but I’ve heard ah-vee-ah-nah, too. Since I say [name]Ariana[/name] as [name]AIR[/name]-ee-ah-nah, AY-vee-ah-nah just sounds most natural to me.
Ay-vee-ah-nah for me too. 
It’s funny that this site lists it with the “ay” beginning because I would automatically go for ah-vee-ah-nuh (and ah-ree-ah-nuh for [name]Ariana[/name]). I think the softer ah sound is prettier, personally. Also, I would assume that the rules of Spanish would generally apply to most names like this and all a’s in Spanish are pronounced ah. I find that the ay or air pronunciations are more Anglicanized, but I think it simply matters how you assert the pronunciation
[name]Ah[/name]-vee-ah-na feels the most natural for me.