Endermites despawn despite being name tagged

Does MC-54556 describe your issue?

Not fully, I was recording on a LAN server and the spectator account used was actually possessing an actual player in front of the endermites, so they were being rendered by loaded player chunks. I also noticed they despawned if I got too far away

The main question is, did you name them with a spawn egg, or name them with a name tag?

I wasn't aware there was a difference, appears that naming them with spawn eggs doesn't stop the despawn timer

Yes there is a difference Naming them from a spawn Egg doesn't stop the timer while name tags do.

Named mobs aren't special, persistent mobs are.
PersistenceRequired stops despawning.

So this IS a duplicate of MC-54556.