There are literally hundreds of hotels in Edinburgh. You'd have to be a lot more specific about the area you want and price range, but to be honest you'd be better just picking one and the worst that will happen is you'll have to meet the girl and escort her to you room. I've been in many hotels to meet girls and never noticed the staff giving a toss who's going to the rooms.
I've only once had an agency ask for hotel details, and that was in Newcastle. There was no evidence of them actually phoning to check. I've never had a girl ask for hotel registration details in Scotland; if she did, I just wouldn't user her. She's not giving out her real name so I'm fucked if I am.
Anyway, you're clearly worrying too much about details. Just book a girl, book a hotel, and get on with it. Good luck, and don't forget to write a report.