Is it OK with most hotels to get a room for 2 people but not confirm who the second person is?
I honestly couldn't say. I'm assuming that hotels care more about "who is in our hotel" than getting the extra dough for two people sleeping there, although I'm sure the latter is a concern. Officially, the hotel would not only want you to pay for it, but also check in your companion. Theoretically, it could be done if the girl was willing to cough up some ID (in reviews of SE Asian countries, you almost always have to check a girl in, and generally that's for your protection as well as the hotel's). In the interests of 'fairness', you could always reserve and pay for the room as a double, but never officially check the girl in.
The two times I stayed in regular Japanese hotels with women, I was with a 'civilian' GF once, and she stayed a few nights with me in my hotel room without checking her in and without any complaint from the hotel, and the other time I had an AM girl come to my hotel in Osaka for a few hours, and she came right up to my room without me having to check her in. Both times they were larger American hotel chains.
I think as I said before some of it depends on the hotel's configuration. If it's a small hotel and/or the reservation desk is right by the elevators, or the elevators require key access to get up to the guest floors, you are going to have a harder time. If you are walking a girl up to your room instead of having her meet you there, you might have a harder time. It's highly dependent on the situation.