Custom Theme – Do I need to change the function.php file?

Not sure where to post this, and not sure how dumb a question this is, but if I am creating a custom theme, and used a copy of the twentyeleven theme to get started, are there files or code I need to delete so as not to cause update confusions?

I have renamed my own theme folder and edited the “head” of the styles.css file accordingly, but I am wondering if I need to do a Find/Replace in files like functions.php for twentyeleven and replace it with my theme name.

Can anyone answer this for me? I want to make sure I don’t leave twentyeleven anywhere and cause myself issues in the future. It seems logical that I would have to remove any istances of twentyeleven in my theme files, but then I wonder if other files reference them and would I have to find/replace in those files too.

Any advice?

Thanks!