Nayanthara is from the Sanskrit nayana (नयन — eye) + tārā (तारा — star) — Star of the eye. Princess Nayanthara — Hindu heritage naming.
Nayanthara 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 Nayanthara reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.