Mumtaz (ممتاز) is the Arabic-Persian word for "distinguished" or "exalted." Empress Mumtaz Mahal (1593-1631) was the favorite wife of Mughal Emperor Shah Jahan — who built the Taj Mahal as her mausoleum, the world's most famous monument to love.
Mumtaz (born 1947) is the Indian actress.
Mumtaz 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 Mumtaz reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.