Attested since 1847, derived from earlier Gorzowa or Gorzowo, which has the same meaning and is attested at least since 17th century. The two most probable etymologies are:
gorzeć(“archaic: to burn, to be on fire”) +-ów. Currently the verb is more often spelled goreć.
gorzeć(“obsolete: to distill”) +-ów. Remnants of this meaning are present in the words gorzelnia and gorzałka, which are still in use.
Before World War II, this was the official name of Gorzów Śląski, a town known in German as Landsberg. After the war, the name was changed to disambiguate it from Gorzów Wielkopolski, a different town also called Landsberg in the Recovered Territories, which had no commonly used Polish name and was renamed by analogy.