Of course, anyone is allowed in hotels in Nepal.That is the answer to your question.If you wanted to say are unmarried couples allowed to stay in the room, well it depends.
Prostitution is illegal in Nepal, we as a society tend to think if any man or woman enter the hotel room it is the sole purpose of having intercourse. It depends from hotel to hotel and who is in the reception at cheap hotels and front office in star hotels.
Normally, if in percentage i think around 40% of the hotels allow unmarried couples as long as you pay in advance and don’t cause a scene.Apart from that there might be many reasons some unmarried couple would want to stay in the hotel.I personally had slept with a girl i hardly knew on a trip to Bhaktapur. It was late night and we could not find any hotels, so we had to compromise and sleep.
It is not necessary that it has to be sex for unmarried people to stay in the same room. Anyway,it is a closed door and what happens inside stays inside unless the moan is too loud for people to hear.
Big star hotels they do not question the status of the couple,anyway they have to fill in the form.If, by chance and it happens mostly in cheap hotels where there were complains of prostitution and the police raid the rooms and find out two unrelated different genders it might be a problem. Mostly they just call the parents and guardians and let them go, in some cases i have heard that they forced them to marry.One person i knew got married with a prostitute..don’t know what happened next.Just be careful not to stay with the under aged girl like 14 -15 without any link of relation.This will cause a big mess.