I don't know when it was added, but shortly after the functionality for naming groups of faces in Android and iOS it is now available on the web interface of Google Photos.
- Click into the "Search" box
- Find a group of faces you want to name. You may need to click "More" to see all of the groups
Click "Who's this? Add a private label to search by name" and give the group a name.
You'll be prompted with names of people in your Contacts and possibly in your Google+ Circles, but you can put any text you want.
Now you can search for that person by the name you have given.
This is also how you can merge two face groups when a single person has been mistakenly identified as two different people.
More information from Google Support.
Do note: Facial recognition/grouping is not available in all countries.