Rasika is from the Sanskrit rasika (connoisseur) — from rasa (essence, aesthetic emotion). Rasika in Indian classical aesthetic theory is the connoisseur who appreciates the navarasa (nine aesthetic emotions) — a concept in Bharata Muni's Natya Shastra (c. Rasika Joshi (1971-2011) was an Indian Marathi-Hindi-Bhojpuri actress — known for Bhoot (2003) by Ram Gopal Varma, Bhoothnath (2008), and Phir Hera Pheri (2006). Maharashtra State Film Award winner.
Rasika does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Rasika reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.