There is a brief acccount in chapter 16 of First Kings about the origin of the name of Samaria.
In verses 23 and 24, we read that Captain Omri, the sixth king of the Northern Kingdom of Israel, who after reigning six years from the city of Tirzah, went on to buy over a hill from an owner called Shemer and built a city on this hill.
Omri named this hill city Samaria, after Shemer, the name of the previous owner. Omri reigned another six years from the city of Samaria before he died and was buried in Samaria. His son Ahab succeeded him. (1 Kings 16:28)
23 In the thirty and first year of Asa king of Judah began Omri to reign over Israel, [and reigned] twelve years: six years reigned he in Tirzah.
24 And he bought the hill Samaria of Shemer for two talents of silver; and he built on the hill, and called the name of the city which he built, after the name of Shemer, the owner of the hill, Samaria.
1 Kings 16:23 - 24 American Standard Version