For other places with this name, see Geneva. Geneva is a city in Ontario and Seneca counties in the U.S. state of New York. The population was 13,617 at the 2000 census. Some claim it is named after the city and canton of Geneva in Switzerland. Others believe the name came from confusion over the letters in the word "Seneca" written in cursive. Geneva's Ontario County portion (which is most of the city) is surrounded by the town of Geneva. The city says it is the "Lake Trout Capital of the World.".