The debtholder is the person or entity that is owed the money. When you owe someone or something money you are the debtor.
A debtholder holds the note or other instrument that identifies the terms of the debt. That note is an asset that, as you point out, can be traded on the market. The debtor owes the holder of the note according to its terms.
As a debtor you have no say, unless specified in the note, who can own that note.
One method of changing the holder of a debt would be to re-finance from another lender. Find a lender who is willing to lend you the money to pay off the current debt and then become a holder of the "new" debt. This assumes the current debt can be settled early; again, something that would be specified in the terms of the current debt.