The explanation for that (according to Wikipedia, https://en.wikipedia.org/wiki/Mitteldeutscher_Rundfunk#History https://en.wikipedia.org/wiki/Mitteldeutscher_R

The explanation for that (according to Wikipedia, https://en.wikipedia.org/wiki/Mitteldeutscher_Rundfunk#History https://en.wikipedia.org/wiki/Mitteldeutscher_Rundfunk#Histo...) is tradition: there was a Mitteldeutscher Rundfunk from 1924 to 1934, when the geographic designation was correct, and the post-1990 MDR just continues that name. Actually, if you look at the map of German regional public broadcasters (https://en.wikipedia.org/wiki/ARD_(broadcaster)#/media/File:ARD_Karte.svg https://en.wikipedia.org/wiki/ARD_(broadcaster)#/media/File:...) and squint a bit, the MDR is more or less in the middle: more on the north-south axis and less on the east-west axis (with only the RBB partly more east), but still...