What is a good "darling" name for hare in Ukrainian or Russian?

Google says that the Russian name for rabbit is "krolik" while the name for hare is "zayats."

If I were to call a daughter or niece "zayats", does a nickname like "Zayatska" or simply "Yatska" make sense? Or is it wrong? If it's wrong, what is a good nickname for someone I want to call a hare?

I call "мій зайчик" - "mii zaichyk" or "зая" - "zaja"

There are other sweet words in Ukrainian - рибка, ластівочка, пташка, кицюня

Oxana.Salij wrote:

I call "мій зайчик" - "mii zaichyk" or "зая" - "zaja"
There are other sweet words in Ukrainian - рибка, ластівочка, пташка, кицюня

Oh, those are perfect! Thank you. :) My heroine's Uncle Vassily will call her mii zaichyk. :) :) :)

Your hero speaks Russian or Ukrainian? in Russian will be "моя зайка" "moja zaika" 

I can help with names if needed

Oxana.Salij wrote:

Your hero speaks Russian or Ukrainian? in Russian will be "моя зайка" "moja zaika"
I can help with names if needed

Ukrainian. Thank you for the offer. :)