dorms are room that you sleep in with more people yeah... you have dorms for 2 or 8 people from 10 to 24...
i remember this from australia, where i always slept in dorms... its not that bad because you meet a lot of other people, that can give you advice, and you can make friends for a live time!!!
you can book it alone, and dont need to book it as a group.
i would advice you to sleep in a dorm, if you want to sleep cheap, dont mind privacy that much, and want to meet people that are in the same situation as you!!!
( this is about australia, but i think this is the same for japan... if im wrong people please ...)