Thanks for the clarification, I understand now. This would indeed be a very useful, but unfortunately, there is no such feature in the SSH protocol - the host name is not transmitted to the server. It might be possible to add a custom extension for it, but that would only work if both the SSH client and SSH server supported it, which is a showstopper for almost all scenarios.
There was a discussion about adding such feature to OpenSSH few years ago (see
https://lists.gt.net/openssh/dev/55943), but it got nowhere (and the suggested workarounds are not really suitable, I'm afraid).