Bender has already had a child, whom the Robot Devil takes in return for letting Bender lead the Army of the Damned.
Bev calls the cops on Bender for kidnapping Ben, when Bev herself is the true kidnapper as Bender had custody of Ben.
Bender gets a Certificate Of Abondonment made by Scruffy. In order for Bender to get the certificate, he must write down the child's name. Bender has already named the child Ben. But later, when he finds out Ben's interests, names him Ben after the first half of Bender's name.