It's not a name but there is a word in Hebrew (really in Aramaic) that sounds like Ayla. ×¢×™×œ×. ayin yud lamed aleph. It means "high." It shows up in Kaddish (Yitbarach v'yishtabach v'yitpa'ar v'yitromam v'yitnasei v'yit'hadar v'yit'aleh v'yit'halal shmei d'kudsha, brich hu. L'eila min kol birchata v'shirata...) - over there it means "higher," I think. I'm sure it's all over the talmud and even tefillah, i'm just not familiar with other examples.
Maybe ask your rabbi about that... But again, it's not a name, so it will depend on your comfort level. :-)