I don't really like
Davina. But I don't think there should be any problem with using another pronounciation than dah-VEEN-ah. Of course you would probably have to tell a lot of people how to pronunce it more than once and probably you would have to explain why you pronounce it like that. But I don't think you should use another pronounciation than the one you really like becuase someone might think that you are "illiterate".
Oh, and I have to defend the parents of
Eva. Eh-va is exactly how you pronouce
Eva in Sweden (and other parts of Scandinavia + Germany)so thinking that the parents "weren't too bright" is in this case a bit, well... narrow-minded. Most common names that are found in the Western world aren't pronounced the same way everywhere.