Fīrūzah
Fīrūzah means 'turquoise', the blue-green gemstone; it is a Persian-derived feminine name used historically among Muslims influenced by Persian culture.
Yes. The word for the gemstone appears in Persian poetry and lexica; as a personal name it is attested in Persianate and South Asian onomastic records.
No. Fīrūzah is not a Qur'anic personal name, though Persian loanwords occur in later Islamic literature.
In Persian/Urdu it is often written فیروزه or فيروزہ; in Arabic adaptations you may see فيروز or فيروزـة for feminine forms.
A masculine cognate is Firuz or Fayruz (فیروز), which also carries the idea of success or is used as a personal name; the feminine form focuses on the gemstone.