During its existence, the city had two names: people referred to it either as 'Dura' or 'Europos'. 'Dura-Europos' is entirely modern.
The Macedonian soldiers who established a garrison station here, about 30 years after Alexander the Great conquered the Achaemenid Persian empire, named it Europos after a town in their homeland. But to the local Aramaic-speaking Syrian population this place was already known as Dura, 'the stronghold'. The people who dwelt in the growing settlement called it by one name or the other. For official purposes, the city generally remained 'Europos'; but colloquially it was usually 'Dura'. In the Roman period, Latin texts usually called it Dura, but Europos also remained in use.
'Dura-Europos', the name by which it is commonly known today, is actually a modern compound created soon after the site's identification in the 1920s. The recent Franco-Syrian mission have advocated reversing this to 'Europos-Dura' to foreground the Macedonian/Greek culture and history of the site, but this has not been generally accepted.
On these pages, I tend to use Europos when talking about the political community or state, but Dura when referring to the place, although use Dura more for the later, Roman history of the city.
A Greek graffito to the Tyche (Goddess of Fortune) of 'DOURA' on the great Palmyrene Gate, the western entrance to the city