If you have access to create your certificates for that server I suggest you create a certificate that includes alternate names that the server may be known as. In that way the browser will automatically resolve the correct name.
From https://blogs.msdn.microsoft.com/varunm/2013/06/18/bind-multiple-sites-on-same-ip-address-and-port-in-ssl/
SAN Certificate (Subject Alternative Name Certificate)
You can setup the wildcard certificate if the domain name for all the
sites are same and first level subdomain changes. What if you want to
set up the sites which should work on two different domain names, for
example, a site with host header as www.testserver1.com and another
site with hostheader as www.testserver2.com. In this case Wildcard
certificate won’t help you. To resolve this issue we have SAN
Certificate.A SAN cert allows for multiple domain names to be protected with a
single certificate. For example, you could get a certificate for
myserver.com, and then add more SAN values to have the same
certificate protect myserver.org, myserver.net and even myserver2.com
or www.example.com.You can see the domain names in the Subject Alternative Name option in
the Certificate