Conny is a distinctive girls' name in United States, ranking #18243 in 2007 with 5 recorded births. The name reached its all-time peak in 2005 with 10 births ranking #10306. Since 1996, the popularity has decreased by 16.7%. In 2007, approximately 1 in every 384,490 girls born was named Conny. FALLING Recent data shows the name is currently falling.