The Joke:
I'd like to be frank with you, but I would have to change my name.
This joke is a classic pun based on the double meaning of the word Frank:
Meaning 1: Being honest or direct (adjective).Meaning 2: The man's name (proper noun).
The humor comes from the "switch." You expect the speaker to be honest, but they pretend you're asking them to literally change their name to Frank.