Social Security records do not have "named beneficiaries." The Social Security Act specifies which family members can receive benefits on your record when you retire, become disabled, or die. Social Security cannot pay benefits to people who do not meet the requirements of the law, nor can Social Security refuse to pay benefits to people who do meet those requirements--even if you ask Social Security not to. But any payments Social Security makes to your former spouse based on your record will not affect the amounts that can be paid to a subsequent spouse or your children.