You can deprecate the whole function which will probably be quite hard to do in your situation but it is possible with some work:
You could check for both, but load the new one for future installs:
function badly_named() {
__doing_it_wrong( 'badly_named', 'This method has been deprecated in favor of better_named_function' );
/**
* Call the better named method
*/
better_named_function();
}