Saba
Yes. Saba appears in the Qur'an as the name of an ancient people/kingdom (the Saba' or Sheba) and a chapter of the Qur'an (Sūrat Saba') is named after them.
Yes, though usage is relatively rare. It has been employed especially in Arabic and some South Asian contexts as a feminine name with historical/toponymic resonance.
Culturally Saba evokes the Sabaean civilization of South Arabia (classical Sheba) and the Qur'anic narrative linking the people to prosperity and subsequent admonition.
The Qur'anic episodes that mention Saba are the backdrop for the later narrative that includes Bilqis (the Queen of Sheba) and her interaction with Sulayman (Solomon).
Common modern pronunciations are /sa.baː/ (Saba) or with a final glottal stop in more classical readings /sabaʔ/; both transliterations are seen in use.