Renaming a theme

OK I know this is probably a stupid question but this is just me making sure.

I need to create a new "version" of the Nelo theme. Simply renaming the folder and css won't do the job, as far as I know you have to rename the theme in the functions.php as well.

The reason I ask is we want to keep things on the site uniform by using the same theme sitewide, but there are changes that need to made to the child blog versions of the theme.

I want to rename the theme to "Nelo2". Could someone please verify wich files I need to edit in order to create a theme called "Nelo2"