If they gave you the current administrator password, than it is pretty straight forward to create a new admin account and name it whatever you like:
1) Go to the blue apple in the upper left
2) Click on "system preferences"
3) In the "system" section, click on "accounts"
4) If the padlock is closed, click it and enter in the admin password to unlock the option pane
5) Click the plus(+) button to create a new account
6) Enter in the new account information, making sure to check the "allow user to administer this computer" checkbox
7) Click "create account"
That's it! Now that you have a new admin account you can log out of the existing account and log into a new, fresh account that still has admin rights. At this point feel free to go back to the accounts window and delete the old admin account.
Hope this helps!
