That is an interesting question. I haven't messed with a H323 phone device in quite some time. For H323 gateways, I believe you can use a DNS name for the Device Name. I can't recall doing it this way in production but it may be worth exploring further. My current lab system is a bit of a mess or I would test this out for you. The idea (theory, if you will) is that if you had different A records in DNS (e.g. myphoneA.company.com, myphoneB.company.com, etc.) that point to the same IP address then you may be able to navigate at least that part of the challenge.
The other thing you could do is that there is a service parameter in CM (Accept Unknown TCP Connection) that allows you to disable the authorization mechanism that CUCM uses. By default, CUCM will refuse to establish H.225 sessions with an entity that isn't configured as a H323 trunk or gateway (not sure about phones). You can turn this off and then the name of the device isn't as important for ingress (egress is still a consideration you would need to handle). I don't recommend turning this parameter off but it may play a role in your eventual solution.
If it were me, I would test out the DNS option first.
HTH.
-Bill
