The phonetic pronunciation of many, perhaps most, of the Maya proper names in glyph inscriptions is generally uncertain, and often unknown. When phonetic data is provided in the glyphs, their ancient pronunciation is often an educated based on modern Maya pronunciation. (There are many dialects of modern Maya, and there is no reason to assume that ancient Maya was not pronounced as differently from modern Maya as Old Anglo-Saxon was pronounced differently from modern English.) Hence, the Preclassic pronunciation of many city names/emblem glyphs and royal names is often unknown, and often very hypothetical.
Only dozen or two Maya personal names are attested in pre-400 AD inscriptions. We need to emphasize that there is probably several thousand times more textual information about Classic Maya as Preclassic. Here is a list in alphabetical order of the major Maya city-states (their names are often Colonial rather than ancient), for which we have sufficient inscriptional evidence to create a king-list of sorts. I’ll include the date of the earliest royal names known from these inscriptions.
Caracol—one mid fourth century king
Dos Pilas—seventh century
Piedras Negras—fifth century
Tikal—seven pre-fifth century kings
Yaxchilan—three pre-fifth century kings
Note that only three of the eleven great city-states have royal names before 400 AD. Here are a list of those kings. Note that the pronunciation of many of the names is unknown, and many are speculative.
1- “Te’ K’ab’ Chaak” (c. AD 350)
2- “Yax Ehb Xook,” (c. AD 90?)
3- “Foliated Jaguar” (2nd or 3rd century AD?)
4- “Animal Headress” (2nd or 3rd century AD?)
5- Siyaj Chan K’awiil (c. AD 307)
6- Une’ B’alam (queen) (c. AD 317)
7- K’inich Muwan Jol “Great Sun Hawk Skull”
8- Chak Tok Ich’aak (Jaguar Paw) (AD 360-378)
9- Yoaat/Yopaat B’alam (c. 359 AD)
10- Itzamnaaj B’alam (“Shield Jaguar”)
11- “Bird Jaguar” (378-389 AD)
A twelfth name can be added: the legendary founding king of Palenque mentioned in the inscription of the Temple of the Foliated Cross, which I will discuss independently later.
Thus, from all of the New World, we have the names of twelve kings before 400 AD. That is a remarkably sparse data base to work with. Basically we have insufficient information from inscriptional archaeology to tell us anything substantial about Preclassic Mesoamerican history during the BOM period (which is precisely why it is called the Preclassic). There is plenty of archaeological evidence to demonstrate that there were many important cities and kingdoms in Preclassic times; we simply don’t know the names of those cities or kings. Thus, again, the problem is not that the BOM somehow fails this test. The problem is that there is insufficient data to undertake that test. If we had for Preclassic Mesoamerica the amount of data we have for classical Greece, and there was no mention of plausible Nephites, that would be decisive evidence against the BOM. But since we lack that quantity and quality of evidence, the methodologically sound response is that the issue is unresolved.