Is Eminem a play on the singer's initials?

Here me out. I don't know why I didn't pick up on it before. His name is Marshall Mathers, intials M. M. When I was young I would always spell his name M&M, I don't know why I didn't pick up on it then. M&M probably would have been copyright violation, so instead of writing his initials, he spelled them out phonetically, "Eminem". Am I right, or am I overthinking it and it's something completely different?

Is Eminem a play on the singer's initials?
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