You can change the Long User Name and the Computer name without any problems. Changing your Short User Name is a bit more tricky, and not recommended.
To change your Long User Name (in Panther), go to the Accounts Preference Pane (launch System Preferences). Click on your account in the left pane and change your Long User Name on the right. You will notice that your Short User Name is not editable.
To change the Computer Name, open the Sharing Preference Pane. At the top, you will see the option to change the name.