First make sure you have a good backup before attempting to make any major changes to your system like changing a user account name.
I don't recommend you attempt this change since the majority of users seem to make a mistake and lose access to their data (sometimes only temporarily), but it is your computer if you are willing to accept the risk of potentially losing access to your data and having to restore from a backup.
Follow the instructions in this Apple article very carefully. One mistake will cause you to temporarily lose access to your data and will require time and effort to restore from a backup (hopefully the backup is good when you restore it).
Change the name of your macOS user account and home folder - Apple Support
As for authenticating to unlock the padlock on the System Preferences is the user account you are using an "admin" account?