as eurocentristic as it gets:

"natio", latin for something pertaining to the descendance/the place of birth/the community of birth, first coined in 1st century BCE as a means to distinguish between (free) people of different backgrounds within the domain of the SPQR). prior to that, natio commonly described an administrative unit, similar to Attic Greek: phyle (community). the Roman Empire was not the first "multinational" (when it came to the ruling class) state, but it was the first state where Civil and political rights were priviledge of one particular nation: Roman citizenship --- originally restricted to (duh) the people of the City, extended to the people of Latium (roughly modern Italy) during the Republic and later, arguably, to all people (in particular the invading ones) in Imperial times - though that last bit does not appear to have helped much.

the "natio" concept reemerged in the wake of modern times with it's meaning shifted towards referring to state territories and economies. concepts of culture, language, ethnicity as transcendent and meaning-giving goods are later semantic additions.

in the old times people mostly identified themselves and others through (duh) the language that they spoke. as common education has not been invented yet, there was, from the standpoint of the individual speaker, usually only two languages in the world, the tongue of the "people common to the land" and the tongue of "the foreigners". it speaks for itself, that neither is to be confused with language in the modern sense.

the marker "Roman", i have just characterized it as a legal marker more than anything else, lost its original meaning in 476CE only to (later) refer to the language spoken in Romanized territories (by the Romanized (free) people), known today as Vulgar Latin. others, primarily of Germanic origin, referred to themselves as "tiut"="the common (free) people" - a word not present anymore in modern languages of Germanic origin (with the exception of icelandic, perhaps), salve in its adjective form "tiutisco/a" = (at one point exclusively) "referring to the language of the common people". as with Classic Latin, noone ever spoke Classic Greek outside of school. in the mediterranian world free people would have referred to themselves as "koinoi" - "common" (plural form to indicate people), and spoke "koine" - the language of the "koinoi", (mis-)identified and canonified as Ancient Greek today. as for exonyms, i am sure beautiful words existed that signify the "otherness" of a foreign language. it doesnt get better than: "barbarians", right?!