There are actually two parts to your question.
Does the superuser account always have uid/gid 0/0 on Linux?
Yes. As is pointed out by Rich Homolka in a comment, there's code in the kernel which explicitly checks for uid 0 when needing to check for the root user, which means that root always has at least uid 0.
Is the name of the user account with uid 0 always
root?
No. root is just a name, listed in /etc/passwd or some other authentication store. You could just as well call the account admin, and the OS itself won't care, but some applications might not quite like it because they expect there to exist a privileged account named root. Calling the uid 0 account on a *nix root is a very strongly held convention, but it isn't required by the system (though it may be required by certain userland software, possibly including system administration utilities).
It's also worth noting that, as pointed out by Simon Richter, on BSDs there often exists a second uid 0 account, by convention named toor (which is "root" spelled backwards, and also lexically comes after root in a list sorted alphabetically). For example, FreeBSD uses it to provide a root user with a customized shell setting, leaving the root user with a default shell which is guaranteed to exist on the system's root partition (useful for recovery purposes).