So, if you have done NO work at all (no edits, no adding metadata, no adding to collections, etc.) on the photos, you could go ahead and delete the photos and then re-import them. But otherwise, re-import is a BAD thing to do, you could lose your metadata, your edits, your collections, etc. So please don't do that.
Renaming photos outside of Lightroom is also a very destructive thing to do, because it essentially renders your Lightroom catalog useless on those photos. They become disconnected inside of Lightroom (or "missing" in Lightroom) and the only way to fix this is one photo at a time.
So, what is the best thing to do regarding the file name IMG_1234-[1-4]? In my opinion, the best thing to do is ignore it.
I had already thought of that but I keep hoping someone from Adobe will tell me that it can't be done.
Thanks for your response,
See this article for how to do more complex file renaming within LR: Complex file renaming in Lightroom made simple(r) – Lightroom Solutions . You could do four renames to remove "-1", "-2", "-3", and "-4".
Thanks for your help dj. Unfortunately I was impatient and made the changes to the pictures and are now ready to send to the customer. But I will try to remember the tool next time.