Note: I’m not British nor American and my mother tongue isn’t English. I pronounce [name_f]Iva[/name_f] as [name_f]EEva[/name_f] (Like [name_f]Eva[/name_f] in English) and EEda. [name_f]Hope[/name_f] it’s clear enough.
Which would you pick? [name_f]Iva[/name_f] is short feminine form of [name_m]Ivan[/name_m], while [name_f]Ida[/name_f] is most obviously pronounced like this due to language.
[name_f]Iva[/name_f] is sweet, but [name_f]Eva[/name_f] is so incredibly popular (and so are [name_f]Evie[/name_f] and [name_u]Evelyn[/name_u]) that I’d definitely prefer the sweet and quirky [name_f]Ida[/name_f] to [name_f]Iva[/name_f].
I like [name_f]Ida[/name_f] (especially with your pronunciation). I always thought it sounded like the name of a Scandinavian princess. [name_f]Iva[/name_f] is very pretty too.