This happened and still happens in my Realm
What I expected to happen was:
I named a Villager so it wouldn't despawn.
What actually happened was:
I left the chunk it was in to find that it had despawned.then when it did, I tested other mobs that could despawn to see if they would despawn when named too, they did. The only mobs that do not despawn are the tamed ones, even the unnamed tamed ones do not despawn.
Steps to Reproduce:
1. Name a mob.
2. Leave the area.
3. Come back to see it had despawned.