No, Aberforth is not a popular name. It is quite rare and not commonly used.
Albus Dumbledore's brother is Aberforth Dumbledore.
Yes, Aberforth Dumbledore ran the Hog's Head.
Aberforth was Professor Dumbledore's younger brother. Aberforth changed his name to Tom so that he can't be associated with Dumbledore and that he can be forgotten.
Aberforth Dumbledore
Aberforth Dumbledore is his full name. No middle name has ever been mentioned.
Aberforth Dumbledore.
He fights in the final battle and as far as we are aware continues to run the Hog's Head.
In "Goblet of Fire" Dumbledore says that "My own brother, Aberforth, was prosecuted for practicing inappropriate charms on a goat." Use your imagination.
Aberforth Dumbledore.
Neither Albus nor Aberforth Dumbledore did.
Aberforth Dumbledore
Albus Dumbledore. Also, his brother, Aberforth Dumbledore, as well as some other family members.