The whole "Cole" language is role-playing the name he uses for his own citizens.
That's an odd thing to suggest. I had no idea his birth certificate said "Tyrant" on it. I always assumed it was "Marcus Cole." You know... his name. His identity. The thing he is called.
But thanks to Golden Girl, let's review the history:
In each and every single thing you quoted, it's someone who doesn't like the guy referring to him by a pet name. I get it. You don't like Cole. You'd rather call him Tyrant.
You can make up names for people as often as you want. For example, I hereby christen you Bean Brain. And I can convince other people to call you Bean Brain too. In fact, I can even change your forum handle to Bean Brain. But would that mean you're not Zombie Man? Chew on that one for a while.
The character in question has two "official" names in the game lore, and by that I mean things that appear on legal documents. One of them is Marcus Cole, and the other is Emperor. Any other documents containing references to him simply call him T3H_DEV1L, but it's hard to take that seriously as what he should be called.