I'd suggest creating a new admin account with your own identity and then getting rid of the original account. Trying to change the name of the current user can, I believe, be troublesome and it's not difficult to lock yourself out of the Mac.
That said, the better overall option, IMO, would be to erase the drive and re-install the OS and in effect start with a new, out-of-the box Mac, as far as users are concerned.
Before doing that (should you choose to do so), there are some things to check before proceeding: e.g. what Mac is it, what OS did it ship with originally, are there two grey install disks with it (there won't be if the Mac shipped with Lion 10.7 or later)?
If the Mac has been upgraded to Mountain Lion (as per your profile) it is likely that it was done using the original owner's AppleID. Doing future updates could be problematic as the OS will be tied to the AppleID, not the Mac.
If it shipped with an earlier OS, that's the one that should be re-installed as that is tied to the Mac not whoever did the upgrade. You can than upgrade using your own AppleID.
This may all sound a bit of a palaver, but it's best to get the Mac totally setup on your ID at this early stage rather than at some point in the future.