Changing your Mac’s computer name:
- Launch ‘System Preferences’
- Click the ‘Sharing’ icon
- Type in what you want your Mac’s new computer name to be
- Close ‘System Preferences’ – it’s that easy
This is how to change what you're looking for. Risk-free and super simple!
That's because his account is still present and you are logged into that. You could remove his and set up your own in Sys Prefs>Accounts. However, there may be some applications or items specific to his account you might want to keep. For the time being, I would suggest keeping his account. Just log in to the new one you create.
In addition, if his account has administrator privileges, you don't want to remove that until you set up your own with same. However, it may be safer to run as standard and keep an admin account around, a new one or his, for purposes of authenticating when required.