Sorry, I should have been more clear. I meant ONCE the tags are correctly set, THEN use Rename (as the OP was asking how do accomplish the rename).
You can use this expression as a Filename rule inside the Rename dialog:
if(Regex([filename (name)], /#^(\d+) - (.*) - (.*)(\.[^.]+)$#/), [R3], Filename(,0))
This will show you the previews of what will be renamed. File names that don't match the pattern are left alone.
If you find examples that don't work, we may be able to modify the Regex() to work with these, or you can reduce the selected files and work with those that do.