Infinity is a distinctive girls' name in United States, ranking #2008 in 1997 with 71 recorded births. The name reached its all-time peak in 1997 with 71 births ranking #2008. Since 1996, the popularity has increased by 54.3%. In 1997, approximately 1 in every 24,516 girls born was named Infinity. FALLING Recent data shows the name is currently falling.