The slightly dog-faced one with floppy dog ears from the original movie Dizzy Dishes
Lean into that. Make an episode where poodle!Betty tries to fit into a human-dominated society but fails to pass as human, with people calling her the B word, and have it end on a cliffhanger as she is prepared for plastic surgery.
Also, the name "Betty Boop" is still under copyright.
Names of characters used in more than one work or in merchandise are generally subject to trademark, not copyright. The US Supreme Court has refused to enforce the Lanham Act, which relates to trademarks and passing off, in such a way that it would extend the effective term of an expired patent or copyright. Kellogg Co. v. National Biscuit Co., 305 U.S. 111 (1938); Dastar Corp. v. Twentieth Century Fox Film Corp., 539 U.S. 23 (2003).