Amrit (अमृत / ਅੰਮ੍ਰਿਤ) is the Sanskrit-Punjabi word for "immortal nectar" — the elixir of immortality. In Sikhism, Amrit is the sacred nectar used in the Amrit Sanskar (baptism) ceremony.
Amrita Pritam (1919-2005) was the iconic Punjabi poet.
Amrit 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 Amrit reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.