The macOS Notes 4.4 allows resetting the password in Preferences. It asks for confirmation first and states that old notes are not affected (initially). Then it asks for your Apple ID passwords once, as it will probably be iCloud synchronized. Then another ‘Are you sure?’ Then enter the new password twice and an optional hint. Note that you do not need the old password to reset things.
Now you can use the old password for old notes, and the new one for new notes. If you enter the new password for an old note, followed by (next try) the old password for the old note, then you will be given an option to change the password for all notes to the new password.

The macOS Notes 4.4 allows changing the password in Preferences. This will be more straight-forward. The password for all notes changes at once. Note that you do need to remember the previous Notes password to set a new one.