Q: how do I change the name of my computer?

system preferences - sharing - computer name - edit...

Here are the instructions from Apple on changing user short name or home directory name. I've used this on a couple of used MacBooks I've bought on eBay. And remember to go into System Preferences>Sharing and change the Computer Name in there.
http://support.apple.com/kb/HT1428

If you know the password of the system admin, perhaps it would be best to create a new account in sys prefs/users, put admin privileges, and thus have your account. When all done, move data from the old to the new account, if need be (via the Shared folder), then delete the old account.

Note that the name in Sharing may be different from this one, usually it is the name detected as the model of your mac. You may change it later, it is no hurry.