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.
The name Layla is derived from Layl (night). The writer of Lisan al-‘Arab wrote: “… Layl might mean the darkest night in the month. Layla also means the first signs of darkness …”
Anyway, Layla is a woman’s name as stated by al-Jawhari and its plural is Layali. On the other hand, many women Companions of the Prophet were called Layla. The Messenger never told them to change this name, although, it was his way to change bad names to good ones. So, since he accepted it and didn’t change it, Layla can then be given as a name to any woman. One should give his sons and daughters good names (that can’t be interpreted to have a bad meaning).
Allah knows best.