Birutė is from the Old Lithuanian biruti (to scatter, sprinkle). Birutė (c. 1330-1382) was the Lithuanian pagan priestess who became the wife of Grand Duke Kęstutis and mother of Vytautas the Great, the most celebrated ruler of medieval Lithuania.
Her tomb on Birutė Hill at Palanga is a national pilgrimage site.
Birutė 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 Birutė reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.