I'm afraid I don't know much, but I'll do some guessing:
ANAYA - "God has answered / answers" would be fine in Hebrew
ARELY - Hebrew "aryeh" means "lion", so where would be "God"? "Or" means "light", so this would leave "ely" for "God" ("eli" meaning "my God"). But the spelling does not convince me. But again if it's American, anything goes.
ITZEL - There is Itzig for
Isaac; could this be a pet form?
JANIYA - variant of Jana/Jean?
LITZY - reminds me of
Elizabeth
Andy ;—)