Based on the OP's comments, here's my thoughts.
First of all, ワ and ヴァ are totally different katakana with totally different sounds at least to the ears of Japanese. Are you a native speaker of (British or American) English who can distinguish the difference between W and V sounds without difficulty? Then all you have to know is that ワ roughly corresponds to English "wa" and ヴァ corresponds to English "va". The difference is very large and important, both in English and Japanese. I don't believe it's a matter of taste.
If an average Japanese speaker who is not familiar with Slovak names (like me) sees Levadnia, they certainly use ヴァ or バ, because they try to read this as an English word. Japanese people have difficulty in distinguishing V and B sounds, so the choice between ヴァ and バ is a matter of taste. ヴァ is not particularly complicated to average Japanese adults, but if you need maximum readability and brevity, バ is a safe choice.
TLDR: You need to seriously think about the difference between レヴァドニャ and レワドニャ. Neither is more grammatically correct than the other, and only you and your wife can decide. If you decide レヴァドニャ is the right sound, you can also use レバドニャ.
-ia can be ～ニア, ～ニャ or ～ニヤ (For example Tania can be タニア, ターニャ, タニヤ). I don't think ～ニャ is particularly childish, but perhaps レヴァドニヤ or レヴァドニア is a bit easier to pronounce.