Muireann is from the Irish Muireann — muir sea + fionn fair/white — sea-fair, sea-white. Muireann is one of the Irish feminine names — central to traditional Irish Gaelic Indigenous Goidelic Celtic heritage. The Irish muir- (sea) compound family is one of the pan-Goidelic Celtic maritime naming heritages spanning Irish + Scottish Gaelic + Manx Atlantic Celtic Indigenous identity.
Muireann 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 Muireann reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.