Changing the comments link produced by the get_comments_link() and get_comments_pagenum_link() functions

So the solution to the get_comments_pagenum_link() function is straightforward enough:

add_filter('get_comments_pagenum_link' , 'new_get_comments_pagenum_link');
function new_get_comments_pagenum_link($content) {
    $content = str_ireplace('#comments' , '#other', $content);
    return $content;
}

Which filters the output of get_comments_pagenum_link() to replace #content with #other, or any other string you might choose.

For the get_comments_link() function, which can’t be filtered, I have simply discovered that my WordPress theme uses it already within its own comments link function, and so have filtered this theme function instead, using the same method shown above.