Writing and speaking duplicated words?

Question

A recent workplace conversation prompted this question. Red Hat, the software company behind a popular Linux distribution, came by the office and everyone got some random trinkets, including a number of red baseball caps with the company logo on it. This led to some amusement about the right way to describe these items, in text and in speech. "I see you're wearing your [x] today", where x is: * Red "Red Hat" hat * "Red Hat" red hat * "Red Hat's" red hat * something else? Is there a rule for these kind of duplicated words?

Answer 1

In this case, "Red Hat" is a proper noun because it is the name of a company so saying someone is wearing his or her (Red Hat hat, red Red Hat hat, Red Hat red hat, etc.) is grammatically correct.