My first name is Lluis but always Ubuntu changes my name as Llus when my computer starts as Ubuntu. I don't understand why this 'i' is missed.
If you just want to change the name that appears at startup, go to System Settings -> User Accounts.
Click the "Unlock" button at the top right of that box. Then click the name to the right, and retype it.
This won't affect your shell/system username at all, only your display name; if you were looking to change the system username too you will need to do something more along the lines of the other answer... though personally I would say it'd be safer to just make a new account and start over in that case; there could be (non-system) files elsewhere that reference your old username in some fashion or other, and these won't necessarily be updated with your new username if you do change it.
Next, as root, run:
Where "old" is your old user name ( Llus ) and "new" is the name you want ( Lluis ).
Log out and back in and you should be good to go.
Note: You might want to use all lower case letters for your user name (lluis) , up to you, see discussion in comments for details.