This really needs to be in the core to be easily accessible to everyone. Along with some other common strings used in comments.
Motivation:
The official hack (given at https://codex.wordpress.org/Customizing_the_Read_More) leads to a loss of functionality (Link no longer sends a reader to a #more-000 anchor). That needs to be handled way better.
Full hack for reference (notice where the link gets botched):
Modify The Read More Link Text
Adding this code to your functions file enables you to customize the read more link text.
add_filter( 'the_content_more_link', 'modify_read_more_link' );
function modify_read_more_link() {
return '<a href="' . get_permalink() . '">Your Read More Link Text</a>';
}