Zaynab, pronounced as (Z)oom + pr(AY) + (NU)m(B)er, which is the name of a "fragrant tree" according to the Arabic dictionaries. It is not clear what tree it is exactly since this is an ancient (pre-Islamic) name. It is the name of some Sahabiyaat (pious women who lived at the time of the Prophet, peace and blessings of Allah upon him and his companions), including one of the Mothers of the Believers (wives of the Prophet), and one of the daughters of Ali bin Abi Talib.
Zaynab is not a Quranic name, but since it has a good meaning and it was used by the family and companions of the Prophet, it is a good Islamic name.
Zaynab can also be spelled as Zainab, Zenab, Zinab, Zeenab, Zeynab, Zeinab.