Syria refers to the current region of Syria, the area north of Israel.
During the time of Solomon, Rezon rebelled and gained independence.
1 Kings 11:25And he was an adversary to Solomon all the days of Hadad, besides the mischief that Rezon did; and he abhorred Israel, and reigned over Syria.
Naaman (Aramean general) was from this place.
Luke 4:27And many lepers were in Israel in the time of Elisha the prophet; and none of them was cleansed, saving Naaman the Syrian.
Hearing the news of Jesus, all the sick and demon-possessed people from this place came to him.
Matthew 4:24And his fame went throughout all Syria: and they brought unto him all sick people that were taken with divers diseases and torments, and those which were possessed with devils, and those which were lunatick, and those that had the palsy; and he healed them.