Bulbul
Bulbul is culturally used among Muslim communities in South Asia but it is not a name derived from the Qur'an or Prophetic tradition; it is a Persian-derived poetic name meaning 'nightingale.'
In Urdu and Persian contexts Bulbul (بلبل) means 'nightingale'; the same script بلبل is used in Arabic transliteration though the word is Persian in origin.
Yes. Bulbul is attested in Persianate and South Asian literary and oral traditions as a poetic epithet and has been used as a given name in Bengali and other South Asian communities.
Common variants in South Asian usage include Bulbula and Bulbulah; spellings vary with local orthographies.
No specific religious restriction exists; it is a cultural/literary name used by Muslim families but not derived from scripture.