Even though its true, you the respective countries had time to develop their own culture & identity and simply labeling it Syria would certainly ruffle feathers

Tbf, your Greater Syria is missing the area around former Antiocheia.

Its very reminiscent of fascist states and entities such as the Greater German Reich and Greater East Asia Co-Prosperity Sphere. It also sounds incredibly chauvinist and nationalistic, because if we’re honest, what does adding “greater” to the front of the name even accomplish?