Mehreen is from the Persian-Urdu mehr (مہر — sun, love, kindness) + -een (suffix). Mehreen Mansoor — Pakistani-American academic. Princess Mehreen — Pakistani heritage naming.
Mehreen 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 Mehreen reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.