Nicknames are often shortened versions that family or friends pick, or that the person prefers. Suggestions of nicknames is difficult, because a "nick" can be totally different from the person's real name, as an example, "Molly" for "Mary".
Here are some nicknames often used in place of Daniel, Danny, or Dan. Note that few are very original; most have been in use a long time.
Most people's nicknames have a connection to something personal about them, or is a childhood nick. If it has a connection, it's often about something a person does, or something specific about how the person acts, or relates to a title the person holds - for example, a Captain of firefighters might just be called "Cap".
A teen boy who
Think carefully before deciding on a nickname. Practice a few nicks out loud at home before choosing one. It's really hard to change a nick once it is used publicly, so be sure you are comfortable with the nickname. Also, think about longevity, meaning, long term. A nickname often sticks with you for your lifetime. You may not want to be a 42-year old "Danny Boy" (except with your wife). Names like "Cap" (for Captain) can "grow" as the person ages.
Danny
Leo the cool lion that's cool
its not
Just the same: Danny comes from Daniel, so any nicknames would be Dan, Dani, Danny, Danielito.
The nickname of "The personification of cool" was given to James Dean.
skywalker
cool man
court
Fifi
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.