Had been routinely running both replica job and backup job on Windows SRV2003 VM. VM was basic server with really no roles. Decided we wanted to run DC Promo on this VM and did so. Also setup DNS, and DHCP role. Once completed, rebooted server and then manually kicked off Veeam backup job. Job failed because the "Server Name Object could not be found". When into Veeam job properties where you select your VM you want to backup, removed the VM listed, and then navigated back to the VM and selected it again. Kicked off backup job and so far now, the job is running.
Did DC promo or any of the other roles I added to this server cause this problem?
No, some other action that you have not mentioned above caused this. VMs are remembered in the backup job with unique VMware infrastructure ID - no operation inside guest OS can change the VM ID.
Operations that triggered the change of this ID include VM cloning, re-registration and such. Additionally, if you added invidual ESX hosts to Veeam console instead of adding vCenter server, having VM moved with VMotion will result in the same issue.