First, read my answer (at least the bold parts), and then act. Since you may want to keep your old files. Or not. There is a computer name (hostname., a username, and a password for that user. Different terms. Read on.
To change the computer name:
1. Fire up a terminal.
2. Type: sudo gedit /etc/hostname
3. Edit the file according to your need, and save it. Close the editor, you are done. (It'll change after a reboot.)
To change the username:
1. Open up the dash (top-left), and search for "User accounts".
2. There is a "Locked" text somewhere. Click on it, it'll ask for your password.
3. Create a new Administrator account.
4. Login to the new one, delete the old one.
! IF ! you want to transfer every setting and stuff from user X to user Y:
1. Fire up a terminal.
2. type: sudo apt-get install mc
3. (when the previous one is done) type: sudo mc
4. Now, mc is a two-pane based file commander. You select files with Insert, and copy them with F5. What you have to do, is copy all the stuff, from folder /home/userX to /home/userY.
5. (you can switch the sides with TAB) Simply navigate the left side, to userX (old one), and the right side to userY (new one). When you are done, use the Insert key, to select all the stuff from the old user. Press F5 when you are done. Enter to confirm.
6. It'll start copying. May take some time.
7. Finally, you need to exit mc. To do that, press F10. (Or Esc and then 0.
8. When you are in the Terminal, again. Type: sudo chown -R userY:userY /home/userY
(Of course, userY is the new user, who you just made for the new owner.)