What Peachey said. To draw further parallels: I lost my car. BUT The car my neighbor stole was mine. She gave me her keys. BUT The keys I found in my bag were hers. There are different forms for when the pronoun is acting as a determiner (my/your/his/her/our/their something) and for when it stands on its own (mine/yours/his/hers/ours/theirs). "His" is the only one with the same form. It's a similar difference like the one between "mi" and "mío" and "tu" and "tuyo" in Spanish.

"Give me their names" is correct. Do you know all our names? Well, I know yours but I don't know theirs.

Model sentences: 1) These are _their_ names. 2) These names are _theirs_.

Like Dario says. Also, note that unlike in Spanish, adjectives in English do not change form for gender or number.