All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
We are not aware of any Islamic prohibitions against the name mentioned in the question "Zanirah".
Indeed, there was a female companion named with a very similar name, Zinneerah. She was a slave and was among the first people to embrace Islam. She was tortured because of becoming a Muslim, but she refused to renounce her Islam. When she became blind, the polytheists said, “It is Al-Laat and Al-‘Uzza [their idols] who turned her blind.” She said, “No, by Allah, it is not so.” So Allah restored her eyesight. Afterwards, Abu Bakr bought her and emancipated her.
Allah knows best.