Assyria is a region in the Middle East mainly including modern-day Iraq, Syria, and Lebanon – though the Assyrian empire once stretched well into Iran, Turkey, Israel, and Egypt as well.
Whether Neville uses the term to describe the region or whether wizarding governments recognize different borders and country names from their Muggle counterparts, this was where his great-uncle Algie got Neville’s Mimbulus mimbletonia (OP10).
It's unclear why Neville uses the term Assyria to describe a region that no longer bears this name. Is Assyria still a country in the wizarding world? And even if it isn't, do wizards recognize different political borders from ours? After all, ministries of magic don't seem connected to Muggle government. What happens when Muggle borders change?