What was Jabba the Hutts pets name?

Jabba the Hutt had several pets. If you are talking about the monkey-creature that sits on his dais his name was Salacious Crumb. If you meant the beast that Luke fought in the pit than that was the rancor. There is also the frog-creature on the stair named Bubo and often the hutt's slave girls are considered as "pets". If none of these answered your question be more specific.