Nicknames usually are part of your name, have something to do with what your are good at or came from a funny story about you.
This isn't really a nickname--just a label as people who read
a lot can be all called bookworms.
However, if they call you Bookworm Jane--
then that might be a nickname. (If your name is Jane.)
For example: Names like Jean can become Jeanie. Someone with a good aim might be called "Eagle Eye". And someone who accidentally ran over a worm with their bike and made a big deal about it might be called "Squash" for squashing worms.
Make this a family activity: Make up a nice nickname for everyone in your family.
This activity promotes creativity.