In the Tags panel, you can right-click on the erroneous name(s) and delete them. Once the wrong name has been deleted, it should not show up in the auto-suggested list and the tags should all be removed from the People stacks.
Before deleting a name, make sure that any photo containing the erroneous tag has been tagged with the correct name. You can do this by checking the erroneous People tag box to see whether any photos have been tagged. You can then tag the photos with the correct name of the person.