While the land that would become known as Samaria was part of the Southern Kingdom of Israel (Divided), King Omri purchased a hill from a man named Shemer. It was that hill where the king began to build the capital city of his kingdom. 

The Name Game
Samaria comes from the Greek name Samareia (Σαμαρεια).
Samareia comes from the Hebrew name Shomron (שמרון).

In naming the city, King Omri not only honored the former owner (Shemer) but selected a fitting name (Shomron) for his kingdom's capital city. Shemer means "guard" while the similar sounding name of Shomron means "watchtower" or "place of watching".

New Testament Times
In 27 BC, Herod the Great expanded, fortified and renamed the city to Sebastia to honor Emperor Augustus of Rome. Sebastia is still the city's name today.