Does the ssh protocol send the remote name to the remote machine?

Question

If I ssh into host3.example.com 192.168.1.1, where host2.example.com also resolves to 192.168.1.1, is there any way for the remote machine to tell which hostname was used for the connection?

i.e. Does the ssh protocol send the remote name to the remote machine, like SNI in HTTPS?

(I am running an ssh server from within an application, so I am free to modify the ssh server to provide this information, if ssh clients provide it.)

Answer 1

As far as I know, there is no protocol extension like SNI for SSH. The DNS name (of the server) is not passed to the server by the client. See also this discussion.