Is this a wrong time to say that I could love to be called by that name

It's okay. We know that Zhenya uses it because he sees Taekjoo as 'weak prey' at first. But actually Zaika (bunny) it's one of the loving Russian nicknames, diminutive suffixes to sound sweet, intimate, or playful. Common, endearing terms for partners, like Kotik (Kitty), Malyshka (Baby), Pupsik (Cutie/Doll)

Yes, I also read about it