Howard gave him the name when he mispronounced "Baba Louie" an animation that Gary was was collecting. Howard goofed on him all day as usual and they thought it was going to end there. It never did.
It now is a popular term that Howard Stern Show super fans use as a greeting or a sign referring to the show and its antics.
It is constantly used when people prank radio or tv stations on the air or on set and yell baba booey.
As a Greeting
. ..Baba Booey to you...
As a prank
Joey Boots :"Baba Booey Baba Booey Howard Sterns Penis Baba Booey"
As a noun
Where is Baba Booey? (Where is Gary)
As a verb
He Baba Booeyed that game. ( to mess up the game as Gary did throwing is infamous pitch)