Green’s Dictionary of Slang

beav n.

[US TV show Leave It To Beaver]

(US campus) a name that indicates that the referent is acting like a little brother.

[US]Eble Campus Sl. Oct. 1: Beav & Wally – names that males call each other in jest, referring to the little brother/ big brother.
[US]J. Lansdale Mucho Mojo (1996) 25: ‘Good night Wally.’ ‘Good night, Beave.’.