Washington (CNN) Sen. Ted Cruz said Wednesday that his re-election campaign was "just having a sense of humor" when it released a radio ad teasing Rep. Beto O'Rourke, who won the Democratic primary, for going by Beto rather than his given name, Robert.

"In terms of the jingle, some of it is just having a sense of humor," Cruz told CNN's "New Day." "We had some fun with it."

Cruz, meanwhile, goes by Ted instead of his given name -- Rafael Edward Cruz.

"You're absolutely right. My name is Rafael Edward Cruz," Cruz acknowledged. "I am the son of my father Rafael Cruz, an immigrant from Cuba who came to Texas with nothing."

O'Rourke, however, declined to respond to Cruz's name-calling.

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