Mus'ab
Yes. Mus'ab is historically attested among early Muslims; notably Mus'ab ibn Umair was a companion of the Prophet Muhammad (peace be upon him).
Literally it comes from the Arabic root ṣ-ʿ-b meaning 'difficult' or 'arduous.' By name usage it denotes someone who faces hardship or is proven under trial.
No. The name Mus'ab is not a Quranic name; its historical notability comes from early Islamic biographical literature about the Sahaba.
Mus'ab is uncommon in many modern contexts compared with names like Muhammad or Ahmad; it is considered rare but recognized among traditional Arabic and Muslim name lists.
As with any name tied to a Sahabi, using Mus'ab is culturally respectful; families often appreciate the historic association with early Muslim exemplars.