A cool nickname for you would depend on what you prefer. This can be derived from your name, your personality or a relevant event that happened in your life among others.
Leo the cool lion that's cool
its not
The nickname of "The personification of cool" was given to James Dean.
cool man
skywalker
Fifi
court
brantie
cool bananas
I think a cool nickname for Madlyn would be Maddie, or you could even use Lyn as your nickname. Maddie is a more casual nickname while Lyn is a little more formal, so it depends on what type of nickname you want to have.
Yes, many people call her 'Chezza'. What a cool nickname.
The cool boy