An excerpt from an ANA piece, in case you were wondering:

Greece objects to the use of the name 'Macedonia' by its northern neighbour on the grounds that it might encourage expansionist policies against Greece. Greeks are also incensed by the attempts of FYROM Slavs to "usurp" the famous Greek general Alexander the Great, whose ancient kingdom lay roughly within the borders of the present-day Greek province of Macedonia, from whom they claim descent.