In my experience there isn’t a way to remove a cloud profile, but you can re-upload the very same one with new saved changes made.
Select it in your local profiles list and click “Share custom profile online” like you did initially. You can now edit the pre-existing name and description if desired. I’ll add an extra “.” or something in description to recognize if the re-upload was successful. You can do this as often as you like.
Note that a copy made of your initial profile will upload as a unique one, so try to use your original one unless you are purposefully uploading multiple versions.