Carmichael is from the Scottish Gaelic Cair Mhicheil (fort of Michael) — historically a Scottish clan surname. Erika Carmichael — American athlete. Tim Carmichael — multiple American figures.
Carmichael 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 Carmichael reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.