The Roman empire did have multiple places with the same name!

One example is Carthage (Latin Carthago), a name which comes from the Phoenician Qart Hadasht, meaning "New City". The Phoenicians weren't as uncreative as English speakers with naming their cities (a quick Wikipedia disambiguation tells me that there are well over 150 places called Newtown or Newton in the world), but they did have at least two cities by this name, one in present-day Tunisia (founded by Phoenicians) and the other in present-day Spain (conquered and renamed by inhabitants of the other Qart Hadasht). When the Romans conquered these cities, they didn't like the ambiguity and called the Tunisian one Carthago and the Spanish one Carthago Nova, "New Carthage". (Yes, that literally means "New New City".)

Such a simple solution would not work for the many Hellenistic cities of the Roman empire that shared names because they were named after Alexander the Great or his successors (especially the dozens of places called Alexandria, Seleucia after Seleucus, and Antiochia after Antiochus). Sometimes a city would have more than one name, if it had been under a succession of different empires/states that called it different things, or if someone wanted to honor a person or event as the namesake of a city (Alexandria Bucephalus, for example, was named after both Alexander and his horse), so that was one way to distinguish. Another way to distinguish was to specify the region or geography of a particular city: Alexandria Eschate (Greek) or Alexandria Ultima (Latin) in modern-day Tajikistan is literally "the furthest-away Alexandria", Alexandria Troas is "Alexandria in the Troad", and Alexandropolis Maedica is "Alexandropolis in the region inhabited by the Maedian people".

That said, in many cases it was not necessary to make those specifications. People in Roman Iberia knew which "Carthago" the inscriptions were listing the distance to because there was only one on the same continent as them. Anyone looking at a map could tell which "Alexandria" the label was referring to because it's a map. Ancient geographical treatises didn't always need to specify because they were already organized geographically, describing a specific region and listing all its towns and peoples in order. Pliny the Elder's Natural History, for instance, includes lots of sentences like

then comes the region of the Ariani, whose town is called Alexandria after its founder