Final answer:
The Magyars became known as Hungarians after they settled in present-day Hungary in the late ninth century and formed a nation-state. Their identity evolved as they integrated into European society and established political structures such as the Austro-Hungarian Empire.
Step-by-step explanation:
The Magyars became known as the Hungarians after they settled in the region that is today known as Hungary towards the end of the ninth century. They were originally a nomadic people migrating from the central Asian steppes. Over time, the name Hungarians became associated with the Magyars due to their settlement in the Carpathian Basin and the establishment of the Principality of Hungary which later evolved into a Christian kingdom under St. Stephen I. The transformation of the Magyar identity was not only a result of their geographic settlement but also a cultural and political evolution as they formed their own nation-state. This transition was solidified as they integrated into European Christendom and established their own monarchy, moving away from their previous nomadic lifestyle. Subsequent events, such as the establishment of the Austro-Hungarian Empire in 1867 and various military conflicts including battles with the Ottoman Empire, continued to solidify their identity as Hungarians.
Notably, after Otto the Great's victory at the Battle of Lechfeld in 955, the Magyars ceased their extensive military invasions of Europe, leading to their settlement and foundation of Hungary. Additionally, the absorption of Hungary into the Habsburg Empire and later the Austro-Hungarian Empire, as well as the modern era's complex political developments including World War II and the Hungarian Revolution of 1956, contributed to the distinct national identity of the Hungarians.