What IamBudman said is true.
One could theoretically check in both the nonflying passenger and the coach passenger to get a boarding pass and then just board as the FC passenger. I do not suggest doing this for legal reasons and that once the coach passenger no shows for the first segment the rest of the ticket will be canceled so they couldn't repeat the process to get home nor could they show up as the coach passenger and expect to be able to fly home as the whole ticket would have been canceled.

While you may have paid for that seat it "belongs" to the traveler and most tickets sold in the US, and much of the world, have restrictions against name changes. You may be able to get a credit in the name of the traveler of the amount you paid for the ticket minus a change fee. But that is also generally restricted to only be used by the named traveler.

If you really want the coach traveler to be in f with you call the airline and see if the person can upgrade.