Why does Bender always say his name after he refers to himself? ex. (Fry old buddy it's me, Bender.)
I see two possible explanations:
Bender is all about name recognition, and will do just about anything to be famous/remembered (see episode "A Pharaoh to Remember", among many others). He likes to repeat his name (and greatness) as often as possible:
Bender is great! Bender, Bender is great!
Bender's ego is amazingly huge! The concept of he has about himself is closer to divinity, Bender thinks that everybody is a sucker and he is the 'Master of Puppets', life is a big game that he plays to win and others are the pawns... and it is true! ;) So talking of himself in third person gives to his words the importance he deserves.
Bender suffers from a disassociative personality disorder so that like Nixon he can deny being associated with his questionable behaviour publicly, "I am not a crook" (Nixon), While continuing to reap the advantages of his aberrant actions privately. His assertion ie. "that was me - Bender" is an attempt to qualify the "real Bender" as an authentic personality thus giving him a feeling of self worth and in a way vindicating the "true" Bender versus his alter ego Bender.