What is the meaning of the name "Hayley" in Islam, and is it permissible to name a girl with it?

The name "Healy" has no origin found in Arabic dictionaries, which means it is not an Arabic name. An Arab Muslim should name their children with Arabic names, as names influence one's personality. As for a non-Arab Muslim residing in their own country, it is permissible for them to name their children with names customary in their country, provided that the meaning is good and it is not one of the names exclusive to non-Muslims.