The Bagman family is comprised of Ludo, Otto, and the father of Ludo and Otto, the unnamed Bagman Sr.
Ludo Bagman is a celebrated Beater for the Wimbourne Wasps c. 1980 and later head of the Department of Games and Sports until his somewhat informal departure from the Ministry in late June 1995.
Otto Bagman got into trouble with the Muggle Artifacts Office because of an unusual lawnmower, but Arthur Weasley straightened things out for him. Out of gratitude, Otto's brother Ludo then arranged the Weasleys' tickets to the Quidditch World Cup (GF5).
"Bagman" = (Eng. slang) While in the U.S. this carries the sense of "one who collects money, as for racketeers", in the U.K. it carries the meaning "traveling salesman."