In short
The area on the other side of the Sea of Galilee was called the country of the Gadarenes
because it was the location of the city of Gadara (on the shore of the Sea), as well as Gerasa, two of the so-called ten Hellenistic cities or the Decapolis (see Matthew 4:25). This area was inhabited by non-Jews.
During the time of Jesus on earth there were a number of large and small cities located to the southeast of the Sea of Galilee. Among the most well-known of these were Gadara (located on this shore itself), as well as Gerasa, two of the so-called ten Hellenistic cities or the Decapolis (see Matthew 4:25). This territory was inhabited by non-Jews.1
28 And when he came to the other side, to the country of the Gadarenes, two demon-possessed men met him, coming out of the tombs, so fierce that no one could pass that way.