The name Eila is a girl's name of Hebrew origin meaning "oak tree". Eila and discussed in our forums with posts like "Which would you choose?".
From the experts:
Eila is a Hebrew name heard in Israel, due for wider consideration thanks to sound-alike sister Isla, as in actress Fisher. Either way you spell it, the name is simpler than it looks: Pronunciation is I, as in the letter, followed by la. An unlikely contemporary name star? Absolutely. But along with other simple names like Ava, Eve, and Ivy, a star nonetheless.