I'm afraid you can't tell Google who the person is, only who the person is not.
- Open up the "People" album where there's a mistake
- Select all of the photos that are mismarked as being for the current person
- In the "More options" menu (three vertical dots) choose "Remove results"
If it all works well, you'll find those photos grouped together under a different "face" that you can rename and have Google identify them again.
For the instance of a person album without a name, just open up the album and add a name. It will draw names from your contacts, but you can include a manually created name as well.
For separate albums for the same person, make sure they're spelled exactly the same. In either case, it will work best if you have a Google Contacts entry for the person. Rename one to match the contact; you should be prompted "is this the same person?" and you can essentially "merge" the albums.