A boy is normal-looking on the left side, but a misshapen green monster on the right side.
Could be a riff on the classic tale of Dr. Jekyll and Mr. Hyde. The a name is a pun on the Beastie Boys, a famous band. The b name is a pun on semicolon, a punctuation mark used to replace the apostrophe in some parts of the sentence.
Beasty Boyd made a brief appearance in the Garbage Pail Kids Animated Series in the segment Savage Stuart: The Garbage Pail Barbarian, which was a parody of Conan the Barbarian. He is seen sleeping at the top of Lord Pondscum's castle until he is awakened by the noise made by Savage Stuart and Corndog, at which point he roars to warn the rest of Lord Pondscum's minions.