Zainab, daughter of Umm Salamah, reported: My name first was Barra. Allah's Messenger (ﷺ) gave me the name of Zainab. Then there entered (into the house of Allah's Prophet (ﷺ) as a wife) Zainab, daughter of Jahsh, and her name was also Barra, and he gave her the name of Zainab.
Muhammad bin 'Amr bin 'Ata' reported: I had given the name Barra to my daughter. Zainab, daughter of Abu Salama, told me that Allah's' Messenger (ﷺ) had forbidden me to give this name. (She said): I was also called Barra, but Allah's Messenger (ﷺ) said: Don't hold yourself to be pious. It is God alone who knows the people of piety among you. They (the Companions) said: Then, what name should we give to her? He said: Name her as Zainab.
Muhammad bin Amr bin Ata said: Zainab daughter of Abu Salamah asked him: Which name did you give to your daughter? He replied: Barrah. She said: The Messenger of Allah ﷺ forbade giving this name. I was called Barrah but the Prophet ﷺ said: Do not declare yourselves pure, for Allah knows best those of you who are obedient. He said: we asked; which name should we give her? He replied: Call her Zainab.
Shaykh Umar Farooq Saeedi
Benefits and Issues: ➊ Praising oneself, that is, being self-congratulatory or singing one’s own praises, is very bad. And this also includes those names in which there is exaggeration.
➋ It is mentioned in the explanation of the meaning of “Zainab” that a large rabbit, a beautiful scene, or a tree with a pleasant fragrance is called Zainab. Some have also said it is (Zain Ab), meaning “adornment for the father,” as a compound. (‘Awn al-Ma‘bud)
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 4953