A divorce decree and a life insurance policy are separate documents, and the policy doesn't read the decree. Three things need handling, and they're handled in three different places.
The beneficiary form comes first because it's the one that pays. Some states cancel a spouse's beneficiary designation the moment a divorce is final. Some don't. And even where there's a law, it doesn't reach every kind of policy. Employer group coverage under ERISA generally follows the form on file no matter what state law says. So file a new beneficiary form and get written confirmation back from the carrier.
Ownership is separate from beneficiary and people miss it. If your former spouse owns the policy, they control it. They can change the beneficiary, take loans, or surrender it for cash, and your name on it as the insured gives you no say. Transferring ownership takes a form and both signatures, which is much easier to get during the settlement than eighteen months after.
Then there's the decree itself. Many settlements make the paying spouse keep coverage in place as security for support. If that's your situation, ask to be named irrevocable beneficiary, or to be made the owner outright. So it can't be changed or lapsed without you knowing. Ask for the annual statement to be copied to you too.
Cash value built up during the marriage is usually marital property. Splitting it can mean a partial surrender. That triggers a tax bill and shrinks the policy for good. A transfer of ownership tied to a divorce generally avoids tax under section 1041. The order of steps matters. I'm a licensed insurance broker rather than an attorney or a CPA, so that belongs with both of yours before anything gets signed.
Once the dust settles, look at whether the coverage still fits. The household changed, the obligations changed, and the amount you bought for a two-income home with a shared mortgage probably isn't the amount you need now.