You posted this in ‘Mac OS X Applications’, so I presumed the desktop version of Notes. My previous description was about doing this on desktop or laptop.
Notes on macOS desktop can share with iOS iPhone, but doesn’t have to. They can be separate. They can be local (non-iCloud). I can’t know your situation without you telling it.
The preference pane for macOS Notes has two buttons
for altering the password: Change or Reset. That is what I described in my previous post, with their subtle difference. Changing (not resetting) the password asks for the previous password
as well, that’s all.