In other words, Hitzig was basically right, except that he was basically unaware that it was the Egyptians who first applied the name of Assyria to Aram, and the term "Assyrian script" to the Aramaic script. The corresponding terms in Greek and Hebrew are derived from the Demotic, directly in the case of Greek, indirectly in the case of Hebrew . None of these terms has anything to do with the history of the Aramaic script. (from Conclusion).
Steiner, Richard C. “Why the Aramaic Script Was Called ‘Assyrian’ in Hebrew, Greek, and Demotic.” Orientalia NOVA Series, 62 no.2, (1993): 80-82.
*This is constructed from limited available data and may be imprecise.