My new MY Passport for Mac is not appearing on the Time machine as an option to back up to

Time Machine will only backup to drives formatted as APFS, nothing else these days. They won’t even show up as available.

Click on Finder and see if the drive shows up as mounted. If it is mounted then check its formatting (Get Info). If not APFS then use Disk Utility to erase and format for APFS.

Check in System Settings for the Allow accessories and set it to Always Ask. Connect the drive and hopefully it will ask if you want to allow it. You can then change that setting to whatever you want.

If your Mac asks you to allow an accessory to connect - Apple Support

Connect a storage device to your Mac

Connect an external storage device, such as a USB drive or Thunderbolt drive, to the appropriate port on your Mac. Identify the ports on your Mac.

• Use a storage device with at least twice the storage capacity of your Mac. For example, if your Mac has 1TB of storage, your backup disk should ideally have at least 2TB of storage. If Time Machine needs more storage space, your Mac will let you know.
• Use your Time Machine backup disk only for Time Machine backups, not for storage of other files.*

The implications being, to connect the drive Directly to the computer and not through a USB HUB

Turn on Time Machine, add a backup disk or change to a different one, or adjust other settings.

There is a very good point made by @ Barney-15E regarding Allow Accessory