Genesee is a distinctive girls' name in United States, ranking #7635 in 2005 with 15 recorded births. This places Genesee in the top 40% of ranked US girls' names for the year. Its actual usage is classified as Rare. The name reached its all-time peak in 2005 with 15 births ranking #7635. In 2005, approximately 1 in every 123,180 girls born was named Genesee. FALLING Recent data shows the name is currently falling.