Albanians are not the only nation in the Balkans to accept Islam. All societies had groups accepting Islam. The difference of the Albanians is that they are the only nation in the Balkans, who managed to have a national identity above religion. Which means that the term Albanian covers all Albanians of Muslim, Orthodox or Catholic faiths.
This is not observed in other countries. This is due to the tradition from the citizenship system in the Ottoman Empire. Officially in the empire, there was not an ethnic system (which was used in almost all Europe), and instead a religious system was used. (Ethnic separation is forbidden by Islam) So there was no use of the term "Turkish". All muslims of the empire, independent of their ethnicity or native language were classified officially under the "Muslim" identity. The term "Turk" was not commonly used, but even if it was used, it was synonymous with Muslim.
Same applied for Christians. All followers of the Greek Orthodox Church, irrespective of them being Greek, Armenian, Bulgarian, Slavic or even Turkish, were classified officially as "Greeks".
From this tradition, the national identities of modern Balkan states are developed in parallel with the religious identities.
Muslim Bulgarians were are not called (and accepted as) Bulgarians but Pomaks. Muslim Slavs were not called Serbians (which only referred to Orthodox Slavs), but only Muslims (and later Bosniacs). Muslim Greeks were not called (and accepted as) Greeks, and these in massive numbers were exported to Turkey after the population exchange between the two states.
During and after the Balkan Wars, all Muslims of the region, irrespective of their ethnic identities, were seen as targets, and most of these were killed or forced to immigrate to Turkey. Out of millions of immigrants to Turkey, a small minority talked Turkish. The remaining populations in the Balkans are in very small numbers.
Albania had managed to transfer from a religious identity into a national identity, which any other nation in the region failed to do. Only Tito's Yugoslavia has managed to keep such an identity for some time, by calling people of the same ethnic background Yugoslavians instead of Serbian, Croatian or Bosniac, in accordance with their religions. But this failed with the fall of Yugoslavia and the tragic ethnic disasters.