Conny is a distinctive girls' name in United States, ranking #15397 in 2012 with 6 recorded births. This places Conny in the bottom 21% 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 10 births ranking #10306. In 2012, approximately 1 in every 293,457 girls born was named Conny. FALLING Recent data shows the name is currently falling.