Tenzin (བསྟན་འཛིན་) is from the Tibetan bstan 'dzin — "holder of the (Buddhist) teachings" — a name traditionally bestowed by senior lamas. It is the personal name of His Holiness Tenzin Gyatso, the 14th Dalai Lama (born 1935) — though this entry covers the feminine usage. Founded the Dongyu Gatsal Ling Nunnery in 2000 in Himachal Pradesh, India — providing rigorous Buddhist education to women that had been denied to them for centuries.
Tenzin 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 Tenzin reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.