I've found what is cause resetting HDMI input names to default.
It seems it's some kind of a feature of Apple TV 4 and HomeKit.
If you added your TV to Home App it will set its own names for HDMI inputs over CEC protocol.
Here is the reddit topic:
Removing TV from Home App resolve the issue.
Hope it helps somebody to close the gestalt and set everything to work as intended.
Good luck!