iPods can be used on as many computers as you like. If it is set to update automatically just connect it to your computer and it will syncronise with your iTunes library and update itself. If you are unfamiliar with iPods you'll find all you need to know to get started on this page:
iPod nano Fast Start: The New User's Guide to iPod nano
You might also want to Rename your iPod. Once you have read the introduction page and have your iPod loaded up just follow the instructions below.
Select your iPod in the iTunes Source list.
Click on it's its name again.
The text box will open for editing.
Type a new name.
Have a look here for more:
How To Rename your iPod
