To a certain degree, yes.
First, you can't change the short name (it's the internal name that the system uses, changing it would result in bad things). Best simply to create a new account for yourself in System Preferences. Make sure that the new account has "Allow user to administer this computer" checked. Then logout, and log back in, this time as yourself. Go to System Preferences and delete the other account (make sure to "delete immediately" if you want to get rid of the old user's data).
Once that's done, the only residual data from the previous owner are probably some of the applications. Don't delete any of the Apple apps in the Applications folder (you can tell if they're from Apple by doing a 'get info', and looking at the copyright field), but feel free to nix any of the others
Given that you don't have install disks, make sure to make a complete backup of your system.