Al-Khansāʾ
Yes. Al-Khansāʾ is attested in classical Arabic poetry anthologies and histories as the laqab of a well-known female poetess whose elegies were preserved in pre-Islamic and early Islamic literary sources.
No. The epithet/name Al-Khansāʾ does not occur in the Qur'an; its attestations are in classical Arabic literary and biographical works rather than scripture.
Originally an epithet describing a physical feature ('snub-nosed'), it evolved into a recognized literary laqab and respected personal name—especially because of its association with a celebrated poetess—rather than functioning as an insult in literary contexts.
It is primarily an Arabic literary/historical name; it is occasionally recognized in wider Muslim intellectual and literary contexts but remains relatively rare as a modern given name.
Her elegies and qasidas are preserved in classical anthologies and cited by medieval Arabic compilers and literary historians; specific manuscript collections and medieval biographical dictionaries reference her poetry.