I googled it (you should always try Google first), and it seems to be a surname as well as a first name. And according to this site (
http://www.thinkbabynames.com/meaning/0/Ailyn), it's derived from
Aileen. I'm a bit skeptical, although it seems to be most commonly used as a Spanish name, so it would probably be pronounced eye-LIN, which is similar to
Aileen. So maybe they're right.