The hostname of the server does not matter and if done correctly should not be visible to the endpoint. However, do not try to rename or change the IP of a connection server. If you really need to you need to have at least 2 connection servers in a pod. You will need to remove it, clean-up the server on the remaining connection server change the hostname and/or IP and then add it back as a new replica server.
The important thing with Horizon is that the certificates work. The name of FQDN that is used to access the servers can be anything that you can issue a cert for and configure correctly. In some cases you may need to tell the connection server to expect the name that you are using.
Can you elaborate on what you are trying to do? Feel free to generalize any specific FQDN/IP/etc...