The Russian word for number is номер. It is used in much the same way as the American version.

Another meaning for it is trick. In my experience this was more a reference to bad behavior.

Этот номер не пройдёт.
This trick won't work.

However, the translation of номер that applies most to my life as a stewardess is hotel room. Four days out of a week I live in various hotels around the country. You would never use "комната" to refer to a room in the hotel.

Иногда номер в отеле большой.
Sometimes the hotel room is large.

Ключ к моему номеру не подходит.
The key to my hotel room doesn't fit.

Я собираюсь остаться в своем номере.
I am planning to stay in my room.

В нашем отеле в Нью-Йорке очень тесные номера.
Our hotel in New York has very small rooms.