If I just saw
Cateline and didn't have any back story, I would probably think it was Cat-a-Line, like a line at the end.
If you want to use the
Kate Lyn sound, and it's just for a story, just use
Caitlin. Who cares if it's too common? Your character isn't real.
I don't like the name
Caitlin or any of its spellings, because I don't like
Kate or
Katie, and I'm not even crazy about
Katherine.