Putting e.g. माया का नाम है as a separate clause like that seems a bit awkward to me. It would flow better if she just said e.g. मेरी छोटी काली बिल्ली का नाम माया है (guessing that Maya is female). If one were to put it separately that way, माया नाम का might be a little more idiomatic (as well as confusing for us non-native speakers).