When a security update is applied as a patch, does the product name change?
I.e. Windows Server 2008
If this server undergoes a patch and/or security update, does it still appear as Windows Server 2008, or does it have to undergo a name change -
I.e Windows Server 2008 version 2, or Windows Server 2008 R2?
No, the installed OS name will not change as the result of a patch. Only an OS upgrade/reinstall does that (and service packs change the service pack level).