Saoirse is the Irish word for "freedom" or "liberty" — a noun that became a given name only in the twentieth century, after Irish independence in 1922. It was associated with Republican politics for decades, and only became widely used as a name from the 1980s onward.
The pronunciation — roughly SEER-shah, though Irish speakers will note nuances no English transliteration captures — has been the chief obstacle to its spread outside Ireland. It is now one of the fastest-rising names in both the U.S. and the U.K.
Saoirse 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 Saoirse reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.