My org deploys a data server and a client device (two devices) in customers' internal networks for them to use our solution; the client device only connects to the data server; however any one customer site may not necessarily provide a static IP or a hostname, nor guarantee the persistence of the devices' IPs. The only things we know for sure we can control are our server and the client device; customers' requirements dictate the network setup.
The client device needs to connect securely to the data server over HTTPS, and we want to provide the option of installing our own certificate using our own CA on the data server. (of the customer can also install their own certificate, but that's beyond the scope of this question)
Since the data server's IP is not guaranteed persistence, I am left wondering, is it possible to issue a certificate to a service, rather than issuing the certificate for the address/name?
I've looked for "ssl certificates for services" and "for variable IPs" and suchlike, but found nothing relevant. Am I missing some terminology to help narrow down my search, or is this just not a thing at all?