Do I need internet to reset my password on my MacBook Pro?

Please read what I said. The only reason you need the internet is iCloud & MDM (Mobile Device Management like JAMF, Kandji, Intune) tied passwords for the whole laptop. People can have internetless Macs. They just won't be able to upgrade to newer operating systems or system updates or download App Store Apps until they connect to the internet. Very few Apps on the Mac require no internet.

Yes you do. Please click on the link below for instructions on how to do it.

Change or reset the password of a macOS user account - Apple Support

The administrator password no. The iCloud password, yes.

The passwords managed by a school or corporation through a managed service provider yes.