A personal library is automatically created for every user. It's the first library in your list by default and it's named with your first name (ie. Ana's Library). Your personal library is your space to create personal notes. You will always know that notes in this library are never shared with anyone else so you'll have the confidence to create any personal notes you'd like there.
The personal library views are optimized for personal notes. So you won't see your profile picture next to each note in the notes list nor in the note view since you already know every note is authored by you.
To share notes you've created in a personal library, just create a team library shared with the people you'd like to share the note with. Then you can simply drag the note from your personal library into a notebook in the team library. Once you do that, it's automatically shared with whoever has access to the team library. You can always later drag it back to your personal library to stop sharing it.
You can't create additional personal libraries. But if you'd like to organize your own notes into multiple libraries, simply create one or more team libraries and don't share them with anyone.