Related from https://bugs.mojang.com/browse/MCPE-22331
Steps To Reproduce:
Rename a mob then re-log. You will see the name tagged mob doesn't save the name after re-logging.
Note:This problem is not affected in the new world.However, it is affected in the world which took over from 1.1.5 and 1.2.0.9 and earlier.
This happen randomly.(Regularity is unknown)
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Are you sure that you're using the newest version of Minecraft? Can't reproduce this in 1.2.0.81.

Yes. This affects 1.2.0.81.
Now I am working so I can not do it, but I will upload the world when I return home.

Bemoty this is pretty similar to a problem we had and I'm not sure if it's duplicate or not. A player in NY realm had an endermite named Pooky and shortly after update Pooky was gone may he rest in peace 🙁

Win 10, xbox and IOS all have the same problem. Jist tested yesterday still an issue in 1.2.

I'm also experiencing this bug with horses and cats in MCPE on Android. 😞

I have a world originally made under Win 10 Beta, and I recently started up again in it using the newest 1.2 update. My horses from before the 1.1.5 update have always kept their names, but everything from that point on will not keep its name.
I tried naming another horse today, and when I exited the re-entered the world, the horse had lost its name.
However, on a friend's realm, I have two cats and two dogs that have kept their names up until the 1.2 update. Sadly, after the 1.2 update, this realm was lost, with everyone, including the owner, was locked out and couldn't get back in and Mojang could or would do nothing to help us get it back.
So I can't say whether or not this bug still exists in this realm, as the realm no longer exists.
But I just tonight checked on another realm, and my horse lost its name not an hour and a few logouts from when I named it.

I am playing on Windows 10 1.2.2 and I had 24 dyed sheep all named. I logged back in today and not a single sheep still has a name. This is playing on a realm world.

This is still an issue and is happening on my Realm with client version 1.2.3 (using Windows 10)..... Animals are not keeping their names after logging off and back on. Also, name tagged items are not persistent and despawn.
Really ruins building a farm!

On our realm, named villagers loose their name tag and then disappear themselves later.

Same thing in my realm, when I name a mob and when I log out and then back in the mob is no longer named.

It's still happening. Used a nametag on a horse in a realm last night, and it was gone the first time I logged in and out (actually, the server crashed). Still waiting to see whether or not the horse itself will despawn like its predecessors.

Still happening with mobs in my realm too - the last victim was a saddled pig which later despawned.
And an interesting curiosity... it also happened to my boat. When it stays in my inventory it keeps its name, but leaving it in the water resulted in the name disappearing on disconnect.

XBox One 1.2.6.2 beta
Named a farmer villager and 2 cats
All 3 names are gone tonight. The villager and the cats are still there, just unnamed.
Thank you for your report!
However, this issue has been temporarily closed as Awaiting Response
Is this still an issue in the latest version?
I was unable to reproduce the problem in 1.2.9 on a Realm (tested with various mobs: Mules, Horses, Donkeys, Llamas and Villagers)
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It appears to be fixed, at least judging by the horse I named weeks ago that still has his name. Now if we could do something about not being able to catch nametags while fishing ...

Just checked on Jeb who I name tag probably like a month ago and he is still name tagged