Najeeb is an Arabic name for boys that means "gracious", "noble", "intelligent". It is not a Quranic name but Muslims can use it since it has a good meaning. It is pronounced [(NU)mber] + [(J)ump + sw(EE)t + (B)oy]. It is written as نَجِيْب in Arabic and can also be written as Najib, Najyb, Nejib in English. It also has a girl-name version: Najiba.
Many names for the mother of Prophet Musa, peace be upon them, are mentioned in books of tafseer, all of them taken from Jewish literature, but none of them are Najeeb to my knowledge, and there is no name for her mentioned in the Quran or hadith.