Rashmika is from the Sanskrit raśmikā (रश्मिका — ray of light, beam). Princess Rashmika — Hindu heritage naming.
Rashmika 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 Rashmika reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.