On PhotoSpring frames there is a screen called the Select Playlist screen. Click here to find out how to get to this screen.
The screen Select Playlist screen looks something like this. 
If you scroll down you'll see a section called People. For every person who sends you photos you will see a different playlist thumbnail for that person.
This help article will describe how to add different playlists in the "People" section. Note: this is not the long term solution, but just a solution until PhotoSpring supports albums.
How to Send Photos Under Different People Playlists
The People Playlists will be labeled by the name of the person who sent the photos. So all you need to do is change the name on the account and the playlist name will also change.
1. In Home Screen of the PhotoSpring Web or Smartphone App tap on the Profile button (circled below) to open a dropdown menu.
2. Tap on My Profile in the dropdown menu that appears. This will take you to the profile setup page.
3. Change the name in the profile setup page to a name that desrcibes the album name you would like to use. Something like "Wedding Photos", "Yosemite 2017" or "Lunch Menu". Tap the Confirm button when finished to save this change.
4. Now you can send photos to the frame and it will place the photos into a People playlist using the name you used in Step 3 above. Repeat steps 1-3 to add other playlists under different names.