Whenever I read about kingdoms or empires in the Middle East or India, they're usually referred to by the name of their ruling dynasty. The Abbasid Caliphate, the Saffarids, the Cholas.
But I've always been curious, is this how they thought of themselves, or are these just western exonyms? How would a medieval Muslim or Indian have referred to themselves or where they're from?
But I've always been curious, is this how they thought of themselves, or are these just western exonyms? How would a medieval Muslim or Indian have referred to themselves or where they're from?
So, to answer this question we first have to separate these two things: the name given to the state, and the identity adopted by the state's inhabitants. In our modern world, there is (at least in theory) a strong overlap between country and identity. I am an American, and I live in America. This correlation was much weaker in pre-modern times. An inhabitant of the Abbasid Caliphate or the Ottoman Empire would not self-identify as an "Abbasid" or an "Ottoman" in a territorial sense, i.e. simply because they lived within and were subject to those empires. Identity was multi-layered and conditional. A seventeenth-century Damascene Muslim notable might identify as a Muslim when interacting with Christians, as a Damascene when interacting with people from another city, as a subject of the Ottoman sultan when interacting with foreigners from another realm, or as an Ottoman when interacting with those less associated with the state and dynasty than him. Above all, the strongest markers of identity were religion, locale, and social status.
For the elites in particular, the last of these was of the highest importance. In terms of cultural identity, the premodern world was noteworthy for its high degree of horizontal integration. Modern society tends to be highly vertically integrated, insofar as most people in the nation, whatever their social class, share a basic degree of cultural similarities propagated through the standardized educational system and through popular culture and the media. In the premodern world, the cultural gulf between the elites and non-elites was much wider, as literacy and education was limited to a small segment of the population. But religious scholars, men of letters, court officials, and state administrators across the Ottoman Empire, whatever their origins (Albanian, Abkhazian, Turkish, Arab, etc.) were all connected by their shared elite culture, carried out in Ottoman Turkish, Classical Arabic, and Persian, languages which most common people would not have been able to understand without difficulty. This elite culture extended beyond the boundaries of the empire. From Morocco to Mughal India, cultural elites shared more in common with each other than they did with the commoners they presided over. That being said, the degree of the elite's cultural isolation and homogeneity is at times exaggerated. Elites were not totally isolated from their localities, and elite culture manifested itself differently in different places.
So, for the Ottoman case, we can turn to specific terminology. In pre-modern times, the Ottoman Empire had no single official name, however by far the most common label was Devlet-i 'Alîye-i 'Osmânîye, or "The Sublime Ottoman State." So calling it "The Ottoman Empire" is perfectly accurate, as they did refer to their state in dynastic terms. However, this doesn't mean that geographical terms were not used. The Ottomans incorporated a wide variety of geographical regions into their titulature. An example is that they commonly referred to themselves as the rulers of "Rûm, 'Arab/'Arabistân, and 'Acem, meaning respectively the former Byzantine lands (Anatolia and the Balkans), the Arab lands, and Iran. The "Sublime Ottoman State" was one which included many territorial entities. In this sense, the name "The Ottoman Empire" can be thought of as somewhat analogous to "The Habsburg Empire," a European state incorporating many disparate geographical regions, united by allegiance to a single dynasty.
The question of Ottoman identity is a difficult one to answer. As I noted above, identities, and the terminology used to describe them, were flexible. The term "Ottoman" ('Osmânlı) was used to refer to those with some connection to the Ottoman dynasty or state. All of the elite, therefore, could be referred to as Ottomans, except for those only weakly under the state's authority. In contrast, a peasant in Anatolia would not have been likely to think of himself in that way. For him, the "Ottomans" would be the state officials and soldiers who collected taxes and maintained law and order. Those with the closest connection to the dynasty additionally termed themselves kuls, or the sultan's "slaves," though that didn't necessarily require them to be literal slaves. Ethnic-regional identity could also play a role, both within and without the elite. Ottoman governors at times formed connections with one another on the basis of shared origin, be it Albanian, Bosnian, Abkhazian, Georgian, or something else. Turkish-speakers (whatever their ethnic origin) from the Balkans and Anatolia were at times identified as Rûmîs, and this is how other Muslims typically referred to them. The terms "Türk" and "'Arab" usually referred to peasants or nomads in the first case, and Bedouins in the second. Historians sometimes term these labels derogatory, though they too seem to have been flexible. We can at least say that educated individuals that we might today call "Turks" and "Arabs" wouldn't have used those terms to refer to themselves during this period, though they did call the languages they spoke "Turkish" and "Arabic."
So to summarize, there's no easy answer here. Identities were complex and overlapping, and historians don't fully understand them either. The tendency to refer to historical Muslim states by their dynasty name is, however, not inaccurate. No Ottoman ever called his state or his country "Turkey" in the pre-modern period, as that word comes from European usage, though they don't seem to have objected to the Europeans occasionally referring to them as such. The state was built around the dynasty, and it was common loyalty to the dynasty which linked the administrators of the empire's territories together, thus the empire bore the dynasty's name.
On identity in the premodern world, there are some relevant chapters in Crone, Patricia. Pre-Industrial Societies: Anatomy of the Pre-Modern World. London: Oneworld Publications, 2003.
On Ottoman identity: