He identifies as a dude but is he a dude without his "equipment"?

All right so I heard of a story of a dude who lost his "little timmy" due to it had to be amputated. He claimed nothing was the same, and I bet. A doc was checking him out and it went like

Doc: Oh, i'm sorry, ma'am! I thought yo-
Dude: I am. I'm a man.
Doc: Oh, so you're transitioning?
Dude: No, I identify as a dude. I just... it's a long story man, can we just get this over with?

And like that it popped in my head, he identifies as a man. Sooo for such a person, would you respect his wishes or think of said person as trans?

He's a dude. Because he said so.
Not a dude anymore, he's a woman.
Uuuuuh (other)
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He identifies as a dude but is he a dude without his "equipment"?
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