Glad you’ve worked it all out. Am even more happy for you that you’ve got your own bedroom!
Personally, I would not feel comfortable pretending to be anyone’s girlfriend. I think what you’ve suggested is fine - you’re just friends. He should respect this, not least because it just makes things so much easier rather than having to make up some silly story about how you met and stave off any further questions about do you want to get married, do you live together, want kids etc etc.