Scripts

I've already tried two options, both with a custom name and with the in-game name, and there's no difference.

Added 1 minute ago
This was also present in the original campaigns and in the Unicorn Empire campaign, in the 4th mission.

Added 5 minutes ago
Do you need a trigger for this?

You just need to give the hero of the player who is not on the map a script. And the name in the script, otherwise I suspect that you entered the in-game name in a completely literal sense. For example, you need to write Arantir, and not Arantir when referring to Arantir in the script.