Given the collapse of the Civilisation, it would make sense to assume that the enforcement of naming conventions, regardless of their genesis, would be far less industrial. This would give way to the more insular conventions of the modern Nations that would have a somewhat more grassroots social evolution at the point we're introduced to them- in medieval Current Day.
I point this out to highlight the significance of folklore and cultural myths and legends, which would have for a good part been intricately intertwined with the territorial geography, given the localised nature of society in each Nation's (A, B, C, D) rise. Taking this stance, the considerations that would have to be made are thus:
- What cultural impact did the collapsed civilisation have on the modern states- that is, did whatever cultural roots that have become amplified over the course of each nation's evolution, take Nation A for instance, regard the collapsed Civilisation as rival or ally?
This becomes significant in considering to what extent they would have allowed the names, and naming conventions, formulated by the Civilisation to withstand the progress of History. A good real-world example of this would be previously-colonised nations reverting place-names to their pre-european titles, post independence. This can be easily gauged by the linguistic influences retained or discarded by each nation.
- What are the socio-cultural/ethical norms, and relationships, facilitated by distinct features of the topography- especially those not precisely within the boundaries of any nation?
In other words, if there were passes through the mountains or trekking-trails through valleys or such, their inhabitants would find themselves less associated with the larger nation-states as much as they would to largely indigenous, or nomadic, Tribes that would pose a higher frequency to these locations. So their customs, and their communication/relationship with nations that the geography facilitates would be far more significant in the naming of these locations. Also, given the medieval setting, it would be these cultural-pockets, so to speak, that were the true catalysts to commerce and cultural trade- giving the ideas fertilised on these routes particular significance in denominations across the entire social/cultural landscape. Think, the Silk Road.
- What is the cultural significance of the topographic features as of the nation that considers it within its territory: does it hold significance as some ethical allusion; do the gods live atop that mountain; did Nation A fight a battle on that piece of land that shares borders with Nation C- further still, was it won or lost?
This is where the relevance of folklore, myths, and legends of each individual nation would really kick in regarding the establishment of geographical identifiers. This would also be a junction conducive to the consideration of border conflicts: what is the all-round acceptance to the claims laid over distinct features of this shared topography by each nation, among the rest; and with whom does most Authority reside- which has the additional benefit of signifying hierarchies in trade and conflict (basically, the economic arena) among the four nations (A, B, C, D) on the map presented.
To sum up, the primary factors of consideration are the History, Language, and Economy of the new Nations; and to what extent they have derived or distanced themselves from the social and epistemological conventions of the collapsed Civilisation.