Katyusha is from the Russian Катюша — diminutive of Yekaterina (Catherine) — from the Greek Aikaterine (pure). Katyusha is one of the Russian feminine diminutives — central to traditional Russian folk and military culture. The diminutive Katyusha is among the most-popular Russian feminine nicknames alongside Dasha and Masha.
Katyusha 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 Katyusha reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.