Edit people albums/tags
Google Photos tries to recognize faces in photos, and makes groups of similar faces. That process is automatic, but all users can remove photos from a group, and in some regions there is also the option to correct or add tags manually.
The following instructions are written for the Google Photos web app, but similar options are available for mobile devices.
Edit the name (tag) of a group
When you hover with the mouse over the name of a group, a pencil does appear. Clicking on the pencil allows to change the name. Confirm by clicking on "Done".
Removing wrongly grouped/tagged people
You can remove photos from a group for several reasons:
not a person
wrong person (users having the option to edit face tags can add the photo to the correct group instead)
not the main subject
blurry or poor quality
offensive
To remove photos from a group:
Select the photo(s) in the group (the option is not available when the photo is opened)
Go to 3-dots > Remove results
The photo will be removed from this group, and hopefully added to another group.
Manual tagging
Manual tagging of faces is not available for all accounts. For example accounts for which face grouping is activated after it became available in Europe seem to miss this option.
You can see whether this option is available when there is an "Edit" icon (pencil) to the right of "People" in the info of a photo.
To add a photo to a group:
Open the photo and the info panel. You should now see the faces that are added to a group, and possibly also the text "n faces available to add"
Click on the pencil. You should now see all the recognized faces. Hovering over the faces in the photo will highlight the face in the info, and hovering over a face in the info will highlight it in the photo. You can now:
Click on a face with a minus in red if you want to remove or correct > select the correct group or click on + in the right upper corner of the screen to create a new group. Select the correct group. You can use the search function to help you. Recently used groups will appear on top, which makes it easier to tag more photos of the same person.
Click on a face with a + in blue if you want to add it to an existing or new group (as described above)
Merging two groups of the same person
It happens that two groups are created for the same person. You can merge these groups as follows:
Add or change the name of one or both groups so that they are identical. Click or tap on the suggested name.
Google should now ask whether this is the same person
Confirm