Answer:
there are many names. to find out, look in your moshling zoo. if you are not a member, look at your friend's zoo. of course, they have to be a member. here are a few names. pooky, honey, tiki, jeepers, blingo. of course, that is just the tip of the iceberg. ( add me! my username is lemmeelove.)
p.s. that is not my real name.
p.p.s. if you did not mean the pets for your monster, sorry. the names are: furi, luvli, poppet, katsuma, diavlo, zommer.