Muriel is from the Irish-Scottish Muirgheal — muir (sea) + geal (bright) — "bright sea." A top-100 US baby name from 1899 to 1930. Muriel (1994 Australian film) — Toni Collette's breakthrough.
Muriel 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 Muriel reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.