Is Naila a permissible name for a girl? Or is it impermissible to name a girl Naila?
People usually hate that name because one of jahilia idols was named Naila but thats irrelevant because the name doesn't express the person and you can't find both good and bad persons having the same name.
The Salaf (May Allah be pleased and have mercy on them) used that name.
We have the Sahabia (female companion of Prophet Mohammad) Naila bintu Salama al-Ansariah, Sahabia Naila bintu Saad and Sahabia Naila bintu al-Farafissa the wife of the 3rd Khalifa Rashidun Uthman ibn Affan.
The Arabic root of the name is An-nawal which means giving and it also has some other good meanings.