Magyar is simply the Hungarian pronunciation of "Hungarian". Its like asking why Germany is called Germany when its made up of Deutsche, why Spain is called Spain when its made up of Españols, or why Finland is called Finland when its made up of Suomi. Another important point, is that the Hungarian word for Hungary is "Magyarország", hence, the people who inhabit "Magyarország" are "Magyars".

great question. official version is the settled europeans mixed the magyars with another raider nation and started calling them hungarians and it stuck on them. the language was not official till the 19th c. and Hungary became independent in the 20th c. why the name Hungary is still around 25 years after this long wanted freedom? i guess it became part of the culture. its tradition. to change it, it would be neccessary to give up part of Hungary's past.

if we can belive Language and Science you can track back the name "Hungary" to the turk "onogur" word ("ten arrows" or maybe "ten ogur/oguz"). Onogur was an alliance of multiple tribes - nomad tribe alliances used to have name structures like "this/that many something". magyars might have been part of this alliance, or they just popped up where previously the onogurs lived, and the name stuck on them. (settled europeans could not really tell the difference between invading nomads: they had the same lifestyle, with constant changing politics they were no real nations, and language itself was far away from having a nation-creating role.)

the name then spread through Europe, one of its ancients form is from the german Ungarn (it has the german "n" ending). it got into most of the slavic languages without the n... and it goes on and on.

note: not everyone calls magyars hungarians. foreign countries use a large variety of names when refering to Hungary: Ungari, Ungheria, Hongire, Hungary, or even Macaristan, Al Magar, Madarsko etc..

so, we still have open questions: who labeled the magyars hungarian? why the magyars did little effort to correct the other nations? the first two written relics confuse us even more:

1.) the first written relic of the magyars is from the byzantine histographer Theophylact Simocatta:

„Hungarians revere fire above all other things; they respect water and air, they praise earth, but they only name one God: the creator of the world. They sacrifice horses, bulls and sheep to Him, and they have priests who – it is said – can tell the future.”

sadly i could not find his original text, the hungarian text says "magyarok" the english text says "hungarians". im not 100% sure, but since both latin and greek (from byzantine) uses the forms Hungaria/Houggaria, maybe he was the first one who clearly labeled the magyars hungarians. anyway maybe he was the first, but not the last who called the magyars hungarians.

2.) Ahmed Ibn Rusta Persian lexicographist and geographist writes around 930:

„Hungarians are of turk race and their leader goes to battle with twenty thousand horsemen. The land of the Hungarians is filled with trees and waters. They have a lot of croplands. These Hungarians are handsome and beautiful people, tall, and wealthy – which they owe to trade. Their clothes are made of silk. Their weapons are laid with gold and silver and pearls.”

again, i was not able to find the original text, but from the presian مجارستان name i guess he used the word Majar or Madjar.

so we can make the confusing observation, that a western scientist (if we count byzantine western) refered the magyars as hungarians and an eastern scientist used his own version. why the western variant was more popular in western europe is no question. this error could have been fixed when Hungary started westernization, but it seems it was not that imortant for the multi languaged ruling class. Hungary took its own name - including other values- from the western culture and used it for international representation.

note the other factors: a) hungarian ruling class always received their high education in greek or latin. b) after the 16th century Kingdom of Hungary was not a sovereign state, the rulers cared even less about the language of the country. c) no one was in the position and really interested at the same time in changing this tradition. d) hungarian language-awarness started only in the 16th c. with Szenci Molnár Albert. his dictionary and article in latin about the hungarian grammar was used as an important handbook till the 18th century. a nice article from Keszler Borbála about this with an english summary at the end. e) magyar/hungarian became the official language of the nation only in 1844. f) major language reforms happened in Hungarian in the late 18th and early 19th centuries.

the article "Hungarian" on britannica.com starts with this: "Hungarian, also called Magyar, member of a people...". some western nations were/are aware that hungarians called/are calling themselves magyars. maybe its a good start to spread the word :)

meanwhile in Hungary, the name of the country was changed in 2011, it went from Magyar Köztársaság(Republic) to Magyarország.

+1 small victory for Magyarország supporters: in 2012, the text Hungary was changed to Magyarország on the olympic outfits.