Vatsala is from the Sanskrit वत्सला (Vatsalā — affectionate, motherly love, loving) — from Sanskrit vatsa (calf/child). Vatsala is one of the Sanskrit feminine names — central to traditional Hindu heritage. Sanskrit feminine name reflecting Hindu bhakti heritage.
Vatsala 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.
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In Pythagorean numerology the letters of Vatsala reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.