Rute is from the Portuguese Rute — Portuguese rendition of Ruth — from the Hebrew Rūt (רוּת — friend, companion). Rute is one of the Portuguese + Brazilian feminine names. Biblical Ruth was the Moabite great-grandmother of King David — central to the Book of Ruth (Tanakh + Christian Old Testament) ancestral figure of Jesus Jewish-Christian heritage.
Rute 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 Rute reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.