I had a similar dilemma w. the Get Together Song (Come on people, smile on your brother, everybody get together time to love one another right now). Some recordings credited it to Dino Valenti. Others to Chet Powers.
One day I had an opportunity to interview The Quicksilver Messenger Service and talked a lot to Dino Valenti, and asked him that question. He told me a story about how he used to ride motorcycles and get stopped by cops, so he developed this alter-ego of .....Chet Powers.
Similar to the Vicki Arnold/Morgan Ames situation.