The correct one is "I have two cats. Their names are Lulu and Fifi." If there was a one cat, it would be right to say "its name (or his/her)". Since there are two, "their names" is the correct answer. I hope this helps Aida!

Their is correct. Plural - two cats. I had one cat who died. Its/his/her name was .... I now have three cats. Their names are ...