Jenice is a distinctive girls' name in United States, ranking #4221 in 2002 with 30 recorded births. The name reached its all-time peak in 2002 with 30 births ranking #4221. Since 1996, the popularity has increased by 36.4%. In 2002, approximately 1 in every 59,894 girls born was named Jenice. FALLING Recent data shows the name is currently falling.