I know we've had questions before regarding who the builders of Teotihuacan were, but I'm looking for a bit more specific detail:
I've heard - both here and in classes I've taken - theories which suggest that the builders (or at least the elite ruling class during the city's height) may have been speakers of an Oto-Pamean language, or alternately Totonacs and Nahua. I assume these assumptions are based on historical linguistic data and/or archeology. I'm interested in knowing what evidence we have, how strong it is, and whether it gives us any strong consensus in the field, or a current leading candidate, for the ethnicity of the city's builders/elites.
(As a note, I'm aware it was a multi-ethnic city at least at its height. I'm guessing that the elites are though to be largely from the same ethnicity, based on other multi-ethnic polities of the time, but feel free to correct me if that's wrong. I'm also aware that the the time period involved is such that modern notions of, say, Otomi self-identification probably don't apply - but any thoughts are appreciated.)
The problem with this question is that nobody really has any idea, so most of the arguments are speculative. Archaeologists are able to distinguish between different material cultures at Teotihuacan. We can see an indigenous population living in Central Mexico that is directly related to prior Central Mexican cities like Cuicuilco. We can also see migrations from other parts of Mesoamerica into specific districts within the city. So we know there was an original ethnic group, and we know that the city subsequently became multi-ethnic. But the ability of archaeologists to address this question really ends there. We can't say what language they spoke, what they called themselves, and what indigenous groups today are descended from them. The other problem, as you pointed out, is that ethnic identities have a tendency to change over the course of thousands of years. Would you call the Gauls "French?" Or ancient pre-Roman Britons "English?" Maybe you could make an argument that there's some continuity, but obviously they're not the same.
Some scholars have suggested that Teotihuacanos spoke Nahuatl (e.g., Evans 2008). This appears to be based primarily on similarities between the pictographic script used at Teotihuacan and the pictographic script used by the Aztecs - including similar conventions for the construction of toponym glyphs. However, a virtually identical pictographic script is used by the Mixtecs, who spoke an Oto-Manguean language. So that argument is rather shaky.
The Aztecs and other Nahuatl-speaking groups of Central Mexico claim to be descended from migrants to the north, and these migrations are believed to have happened around the Early/Middle Postclassic (between 900-1300 AD, more or less). If that origin story is true, then the builders of Teotihuacan likely did not speak Nahuatl. This has been corroborated by modern linguistic studies (e.g., Justeson et al 1983). Historical linguists and epigraphers looking at other Mesoamerican languages - including Maya hieroglyphic inscriptions - have found no evidence of loanwords or other influence from Nahuatl on Mesoamerican languages dating prior to the Postclassic period. This suggests that if Nahuatl speakers were living in Central Mexico prior to the Postclassic, they weren't impacting the development of neighboring languages very much. Given the influence of Teotihuacan on material culture, it seems likely that there should have been some kind of influence on language.
So if they didn't speak Nahuatl, what language did they speak? Well at this point it's anybody's guess. Mesoamerica is a hodgepodge of different languages in different language families. It could have been anything. Most of the other (non-Uto-Aztecan) languages of Central Mexico, such as Otomà and Mazahua, are in the Oto-Manguean language family. (For the sake of reference, see this map, the red on the map is the Nahua-speaking migrants). So it seems probable that Teotihuacanos spoke some kind of Oto-Manguean language. The Totonac people today claim that they built it. That's also possible, as powerful Totonac sites like El Tajin arose immediately following Teotihuacan's collapse. But the Totonacs don't live in Central Mexico today - they're primarily on the Gulf Coast. If they were the original ethnic group of Teotihuacan, how did they end up in a completely different region a few centuries later? Furthermore, Totonac sites of the Epiclassic/Early Classic show as much continuity in material culture with previous cultures on the gulf coast as they do with Teotihuacan.
So we can say with some confidence that the Teotihuacanos were not Nahua, but beyond that there really isn't any strong evidence as to who they were or what language they spoke. The arguments presented for one group or another are speculative, and there isn't a lot of hard evidence to back them up.
Evans, Susan Toby. 2008. Ancient Mexico and Central America Thames and Hudson Press.
Justeson, J. S., W. M. Norman, L. Campbell, and T. Kaufman. 1983. The Foreign Impact on Lowland Maya Language and Script. In Highland-Lowland Interaction in Mesoamerica. A. G. Miller (editor). Dumbarton Oaks.
:D Just a side question: anyone knows what the original Maya name for the city was? I read somewhere that Teotihuacan was the Aztec name for the by the already deserted city.