I'm running El Cap, having manflu, started tagging Faces on the Macbook, moved over to the Big Mac and surprise... I'm doing it again... so it's not a question of betas, I just hope they fix it.
The weird thing is that if I go back to the Macbook and search for the name, it shows as "John Smith – Face". It only doesn't show among the "bubbles". This doesn't sound like something incredibly difficult to fix...
I have the exact same issue. About a month ago or so I ended up having to reinstall OS X El Cap on my MacBook Pro and found out that my Time Machine backup was corrupted (fun, fun)...I didn't mind so much as everything that's important to me is backed up to the cloud at this point, including Photos. Well, I had no idea about Faces albums not being stored in the cloud, so I was quite panicky when I went to tag some faces this morning and found that my Faces album was completely empty. When I searched for peoples' names in the search bar, the results were still there (i.e. searching for "John Smith" displayed the correct number of faces already tagged for him), even though there was no John Smith "face" in the Faces album. So, I was glad that the data was still there, at least, even if it wasn't being displayed in the normal way.
So now I have a bunch of new photos to tag, and guess I'll just tag them as new Faces with the same name as previous Faces. I guess that means that I'll potentially have to merge duplicate Faces with the same name when Sierra comes along, from what I've read here, but I guess I'd rather do that than lose all my tags altogether. I'm glad to read that Faces (or I guess, now, People) still allows you to manually tag people. I'm a bit obsessive and have a rule about tagging everyone in a photo, even people who might be partially obscured or unclear.
@navaira, what I would probably do if I were you, (if you're planning on upgrading to Sierra in the fall), is just do all the tagging on one Mac for now, since it seems like this work will eventually sync to your other devices once Sierra is ready. That way you wouldn't end up having to do the same work twice if it does work, and if it doesn't sync the way it should, at least you'll know for sure before doing all the work.