Consequent to Divorce, Employee is entitled to File Fresh Nomination.
From India, New Delhi
As suggested by seniors in the forum, intimating the Organization is not important as it is his/her personal affair.
Your concern raises if the spouse's name has not been changed later for his claims in either EPF,ESI,Gratuity etc.
Only option available to the company, if the claims come is to get the legal succession certificate by the claimants and pay,even if one claimant comes or two come.
From India, Hyderabad