Booking.com wasn't recommended as a means of booking your hotel. People have used Agoda successfully. I just messaged a few hotels and depending on their response I made my decision.
I just noticed you have free cancellation, maybe better to cancel booking and deal directly with hotel. I emailed and messaged a few hotels and picked the one who responded quickly and efficiently and took it from there
You need both names on booking confirmation as it is required when filling out separate Thailand Pass for each person. Check with booking agency if it was for 2people.
When you enter with tourist visa you are permitted to stay for that 60days plus if you want you can extend for another 30. So a change of plans on your part wouldn't be a problem in that timeframe.