In the comics, the individual Beagle Boys are referred to by their prison numbers that are printed on their chests. The three most common numbers are 176-167, 176-671, and 176-761.
On Duck Tales they have names and different personalities like Bigtime, Burger, Bouncer, Baggy, Babyface, Bugle, and Bankjob. The usual character combination is Bigtime, Burger, and Bouncer, and sometimes Baggy or Babyface, Bugle, and Bankjob. Their Leader is usually Bigtime or Bankjob or their mother Ma Beagle.
The Beagle Boys have lots of relatives who count each other as brothers and cousins: apart from Ma Beagle there are the Beagle Brats (sons or nephews), the Beagle Babes (older generation which happens to be a trio of female cousins and a younger generation which happens to be their daughters or nieces) and their grandfather Blackheart Beagle.
According to Don Rosa's Life and Times of Scrooge McDuck, Scrooge first met The Beagle Boys in his Mississippi riverboat days. Those Beagle Boys included Blackheart Beagle and his three sons. Scrooge first met the modern Beagle Boys during Christmas 1947, which was when he first met his grandnephews Huey, Dewey, and Louie and met his nephew Donald for the second time. Since then the Beagle Boys have been a constant threat to Scrooge's huge money bin.