Forseti's name did not fade from Icelandic vocabulary the way many other minor Norse deities' names did; instead it took on an entirely new, secular life. Modern Icelandic uses the word forseti as its standard term for a presiding officer or chairman, and, most prominently, as the title of the President of Iceland, forseti Islands, so that the head of the modern Icelandic republic bears, in an entirely secularized and etymological rather than religious sense, the name of the old god of justice and reconciliation.
The semantic path is transparent: forseti is built from fyrir, before or in front, and sitja, to sit, meaning literally one who sits in front or presides, which describes equally well a god enthroned in Glitnir settling disputes and a modern official presiding over a parliamentary chamber or a nation. This linguistic continuity is not itself evidence of any continuous religious veneration of Forseti across the intervening thousand years of Christian Iceland, the word simply preserves an old descriptive compound whose most famous ancient bearer happened to be a god, but it does mean that the concept Forseti embodied in the mythology, a calm, impartial authority who presides and reconciles rather than commands by force, remains linguistically alive in Icelandic civic life in a way most of the old pantheon's names do not, encountered today by ordinary Icelanders not in a saga but on the news, attached to their own head of state.