Two episodes revealed that Pumbaa's last name is Smith. This was likely meant as a joke due to how incredibly common Smith is as a surname. Pumbaa was also a member of a group of warthogs but by the time he was fully grown he was banished because of his smell, which was apparently appalling even by warthog standards (similar to how Pepe Le Pew's stench is often shown to be by skunk standards).
In the television series, Pumbaa had an uncle whose name was Boaris, and lived in Russia. Apparently, Boaris was really good at ballet, but then, because of Timon, he fell on fish eggs and went to the hospital and Pumbaa was dancing the ballet, but he broke his leg, then Uncle Boaris comes to dance. Pumbaa also had a deceased uncle named Ernie, who told him that he had to believe in himself to catch bugs.