Triin is from the Estonian Triin — Estonian rendition of Katriin / Katrin — from the Greek Aikaterine (pure). Triin is one of the Estonian feminine names — central to traditional Estonian + Baltic Catholic + Lutheran heritage.
Triin 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 Triin reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.