What is this thing? It was shown in Jabba's Palace, sitting with Jabba, and seemed like it was probably some sort of favored pet.
Is it sentient? Does it have a name, or an identified species?
That is Salacious Crumb. To quote the Star Wars Wiki:
And yes, Jabba the Hutt has a full name.
Regarding their sentience, the Star Wars Wiki says:
I believe it's a gremlin like creature that jabba found and kept as long as he pleased.
He looks like a gremlin also so that jabba apparently thought was cute like a puppy so kept it.