Pyrene (Πυρήνη) is from the Greek pyr (fire). The princess of Bebryces, beloved by Heracles, who died alone in the great mountain range — the Pyrenees mountains are named after her. Heracles raised stone cairns over her body that became the peaks.
Featured in Silius Italicus's Punica.
Pyrene 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 Pyrene reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.