I think Delta Vega being in the Vulcan system is PLENTY enough to establish that this is a totally different universe.
Pick up an atlas. Do you have any idea how many duplicate town names there are in the world?
Why would the galaxy
be any different?
(Yeah, I'm aware it was a "cute reference" to TOS that's largely unappreciated, but it's also one of the easiest "issues" fixed/explained/glossed over/ignored)