Can't guarantee the ID, although it does fall into the very broad nicknamed species of Old-Man cactus. The clumping feature is more like a mammillaria type but not sure. Regardless of the ID, I would change the soil to a more fast draining soil than what it is in now, like a mix of C&S soil mixed 50/50 with perlite or pumice. The soil it is in retains too much water. Also it would be better to have it in a clay pot than plastic. Whatever pot you end up using, I would definitely take the secondary container out. The set up in your pic prevents good drainage and could lead to root rot. Also your cactus needs a lot of light. Enjoy your cute little old man :)