Thank you for your reply. I'm looking for not only English spellings, but British, if that can even be applied.
I suppose at some point other languages adopt their own versions of names, so I don't know if this issue has come out formally among the Nahuatl-speaking community. Presses seem to have rules, but they vary.
As others have noted, the use of the accents reflects the need to place accents based on current Spanish speakers' pronunciation. The rules of Nahuatl dictate something different. In many place names ending with -tlan or -tan, modern pronunciation places the stress on the last syllable, thus needing an accent in the rules of Spanish. But this is not the case in traditional Nahuatl pronunciation where the accent was ALWAYS on the next to last syllable (yes, except for vocatives and a very few other instances). So, in general I do not use accents on Nahuatl words.
The samples you mention, Some examples are Teotihuacán, Tenochtitlán, Copán, Chichén Itzá, Uaxactún, Kabáh, and Yaxchilán.
are accented for Spanish. Nahuatl speakers would say Teotíhuacan, tenochtítlah (the "n" is nasalized and hardly, if at all heard) etc..... I do not know about the Mayan words.
If your press wants to give readers a version of the original indigenous spoken word, I would argue for the samples I have shared.
If you are wanting to show how they are said in modern Spanish, then there would be no need to change the orthography.