First of all, which major-mode are you using comment-region in? I'm surprised because here in C/C++ mode the comments of comment-region already look like //... by default and it has alwas been that way.
When I currently run this function I get commented out lines that look
/* like */
/* this */
Is it possible to configure this to use "C++" style single lnie
comments so they would look
// like
// this