What are you? Insane?
Of course it was rape. What kind of a stupid question is that?
Assuming the events went down as chronicled (the usual disclaimer), there's no other name for it.
In summary: a woman excuses herself from a party and goes to sleep in the bed of her sometimes-lover. The lover's identical twin sneaks in to the room and has sex with her. Something seems wrong. Some subtle cue throws her off. She turns on the light and realizes what happened.
And someone has to ask, "Did the mistaken identity negate her consent?"
Of course it did. Imagine this instead. A man and a woman are having consensual sex like they have on the Discovery Channel. While the woman is facing away, the man pulls out and a second man - hidden until this moment - slips in and penetrates her.
Is that rape? Damn right it is.
The analogy is coherent and obvious. She generally consented to sex with her lover. Drunk people can have sex without it being considered rape when they have such an arrangement. Drunk people with no such prior arrangement don't have that luxury. She consented to sex with her lover and was fine with him slipping in to the room. She did not consent to sex with his brother.
There was a question? Seriously?