Conservatives are the ones hung up on names, not liberals, and there were some who picked on Jimmy Carter for not using his given name of James to sign official documents, they thought it was too informal.
And we know all about Barry Soetoro, ooooh a nickname. You'd think it was Hitler or something.
Cruz's first name is Rafael, a lovely name, but way too Hispanic for the image he's trying to project, and the nickname for that is Rafe. Not Ted, which is a nickname for his middle name. And nice and Anglo sounding.
The reasons behind William using Bill, and Rafael using Ted are very different.