Regarding hard coding a header into the default theme

Hi I am referencing this support page
In the answer by aecnu to the issue it is said that the function.php file is modified and can reside in the child folder. I have modified the framemarket function.php file and not the child function file since the code he references does not appear in the gridmarket function.php.
My question, since there is already a function.php in the child folder will putting the framemarket function.php file in the child folder create problems since both files will have the same names. Also should the original framemarket function.php file that resides in framemarket be deleted.