The Estadio Azteca no longer exists under that name, and behind the new one sits a commercial operation that most people never see.
What a naming-rights deal actually is
It is a trademark license plus a bundle of advertising obligations. The sponsor pays for the right to have its registered mark applied to the venue, used in broadcast references, printed on tickets and signage, and defended against unauthorized use. The venue owner undertakes to use the new name consistently and to require third parties to do the same.
The value depends entirely on the mark being registered and enforceable. A license over an unregistered name is worth very little, because there is nothing to stop anyone else using it.
Why the old name does not simply vanish
Decades of public familiarity do not transfer by contract. Broadcasters, fans and journalists keep using the historic name, which is why these agreements contain detailed clauses on how the venue must be referred to and what the operator must do when it is not.
The takeaway
If you are licensing your brand to anyone, the license is only as strong as the registration behind it, and it should specify exactly how the mark is to be used and what happens when it is misused.
Renaming an asset that already has equity
Changing a name does not move the rights. The old registration keeps protecting the old name for its remaining term, and the new name is a new application, examined from scratch against the grounds in article 173 of the Mexican Industrial Property Law.
So the sensible sequence is to file the new name first and keep the old registration alive in parallel, at least through the transition, because that is when third parties test whether the old name has been abandoned.
Keeping it alive is not automatic: each registration needs its declaration of real and effective use at the third anniversary, and the renewal runs from the date of grant (articles 233 and 178). A name you stop using is a name you eventually stop owning.