After factory reset, how do ensure that my Apple ID will not be required for any functions on the Mac Pro after factory reset

What to do before selling or giving away your Mac - Apple Support

If your computer came with Snow Leopard or earlier installed, then stop the above at Step 5 and do the following instead:

Clean Install of Snow Leopard

1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came

with your computer. Insert the disc into the optical drive and restart the computer.

After the chime press and hold down the "C" key. Release the key when you see

a small spinning gear appear below the dark gray Apple logo.

2. After the installer loads select your language and click on the Continue

button. When the menu bar appears select Disk Utility from the Utilities menu.

After DU loads select the hard drive entry from the left side list (mfgr.'s ID and drive

size.) Click on the Partition tab in the DU main window. Set the number of

partitions to one (1) from the Partitions drop down menu, click on Options button

and select GUID, click on OK, then set the format type to MacOS Extended

(Journaled, if supported), then click on the Apply button.

3. When the formatting has completed quit DU and return to the installer. Proceed

with the OS X installation and follow the directions included with the installer.

4. When the installation has completed your computer will Restart into the Setup

Assistant. After you finish Setup Assistant will complete the installation after which

you will be running a fresh install of OS X. You can now begin the update process

by opening Software Update and installing all recommended updates to bring your

installation current.

5. If you are planning to sell or give your computer away, then do the following:

After you reformat your hard drive and reinstall OS X, the computer restarts to a

Welcome screen and asks you to choose a country or region. If you want to leave

the Mac in an out-of-box state, don't continue with the setup of your system. Instead,

press Command-Q to shut down the Mac. When the new owner turns on the Mac,

the Setup Assistant will guide them through the setup process.

You must always replace your system with a fresh version of the system that originally came pre-installed on the computer. Are you saying Yosemite was the original version installed when the computer was new?