Aislinn is a beautiful old Irish name everyone seems to think it comes from the name aisling but this is not true. Aisling is a newer version of name Aislinn it is pronounced as ash-lynn not ashling or ashleen.
Sorry to burst your bubble, but "Aislinn" doesn't mean anything in Irish, old or modern. "Aislinn" IS a just a corruption of the word, and later, name, Aisling which means "vision" or "fantasy", not just an ordinary dream. And the pronunciations ASH-ling and ASH-leen, as opposed to just ASH-lin, arose because of differences in the pronunciation of Irish across the four provinces. Neither one is more correct than the other. I have done some research, and the oldest form of the the word "aisling" I can find is "aislinge" (middle Irish). "Aislinn" is definitely modern invention/mutation, not an older spelling of aisling. I would seriously question your proficiency in the Irish language.