The payouts and recipients of the income are part of something known as the annuity structure.
The owner enters into a contract with the insurance company for the annuity.
The owner can then choose to be the recipient of the income (known as the annuitant) or they can designate someone else to receive that income.
The owner can also decide if there will be someone to receive the subsequent income once the annuitant dies (known as an annuitant beneficiary).