Is it grammatically correct to say "someone being a mood "?

@Elliot in the comments is correct for "normal" usage, the preposition in is used with "mood", or you can use the adjective moody.

However, recent slang does use "mood" without a preposition. The most common way might be attached to a picture, illustrating said mood, as explained by Daily dot and Slate.

This can also take the form of "x is a mood", e.g. "Michelle Obama at the Oscars is such a mood". However I have never heard it in the form you describe, "... being a mood", typically the formula is just "is a mood"