I did this, I think with some help from some posts here.
Make sure both drives are connected & then launch Disk Utility. Click on one of the drive names in the left column (the main drive icon, not a sub-icon) & click the Restore tab across the top (far right). Then drag the icon of the older/smaller drive to the Source field & the icon of the new drive to the Destination field & click Restore. I found it worked best with Erase Destination checked, which is not a problem with a brand-new drive. When this is done copying & verifying (at least 2-3 hours!), the new drive will have the same name as the old drive.
Then rename the old drive & then open the Time Machine preferences & make sure it knows to use the new drive.