Yami (यमी) is the feminine of Yama — "twin." The twin sister of Yama, god of death — in Rig Veda 10.10, she tries to persuade her brother into incest to perpetuate humanity (he refuses).
Featured in Rig Veda 10.10.
Yami 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 Yami reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.