The income tax answer is clean, and the estate tax answer is not. Section 101(a)(1) provides that "gross income does not include amounts received (whether in a single sum or otherwise) under a life insurance contract, if such amounts are paid by reason of the death of the insured." A beneficiary who takes a lump sum owes no income tax on it. But section 2042 reaches the same money for estate tax purposes, including it in the insured's gross estate "to the extent of the amount receivable by the executor" and, for other beneficiaries, to the extent the decedent "possessed at his death any of the incidents of ownership." Owning the policy on your own life, and therefore being able to change the beneficiary or borrow against it, is enough. The two questions have separate answers, and confusing them is the most common error about life insurance in an estate plan.
A second tax point, less known and easy to walk into: section 101(a)(2) caps the exclusion where a policy has been transferred for valuable consideration, limiting it to what the transferee paid plus premiums paid afterward. There are carve-outs, including transfers to the insured, to a partner of the insured, to a partnership in which the insured is a partner, or to a corporation in which the insured is a shareholder or officer, and a further rule turning the carve-outs off for a reportable policy sale. Any transaction in which a policy changes hands for money deserves advice before it happens rather than after.
Divorce is where the law splits in a way that catches people out, and stating it nationally gets it backwards for half the country. Many states have adopted statutes that automatically revoke a former spouse's beneficiary designation on divorce; the Supreme Court counted 26 of them in 2018 as having adopted revocation-on-divorce laws on the Uniform Probate Code model, which reach nonprobate assets such as life insurance policies. For an individually owned life insurance policy those statutes apply, and the Supreme Court upheld applying one retroactively to a policy bought before the statute existed in Sveen v. Melin (2018). For employer group life insurance, which is an ERISA plan, they do not: in Egelhoff v. Egelhoff, 532 U.S. 141 (2001), the Court held that Washington's revocation-on-divorce statute "has a connection with ERISA plans and is therefore expressly pre-empted," because it "binds plan administrators to a particular choice of rules for determining beneficiary status." The policy in Egelhoff was the decedent's employer-provided life insurance, and his ex-wife was paid. So a reader with workplace coverage who assumes the divorce already fixed the form is the one at risk, and the fix is to file a new designation rather than to rely on the decree.
Naming mechanics on a policy. A designation can be primary or contingent, can split percentages among several people, and can specify what happens if a named beneficiary dies first, which is what per stirpes and per capita language does. A designation can also be made irrevocable, in which case the owner gives up the unilateral right to change it and needs the named beneficiary's consent, a structure that shows up in divorce settlements where the policy secures a support obligation. Whether a designation is revocable is a contract term, so it is worth reading rather than assuming.
Two constraints that come from outside the insurance contract. First, minors: an insurer will not pay a death benefit to a minor child, and NAIC says so directly, advising against naming one because "insurance companies won't pay a minor" and pointing the owner to an estate or a trust instead. The alternative to a trust is a custodian under the state's transfers-to-minors act, or a court-appointed guardian of the property, which is the outcome nobody chooses on purpose. Second, marital property: in a community property state, premiums paid with community funds can give the other spouse an interest in the proceeds even when someone else is named. California's Family Code section 1100(b), for example, provides that "a spouse may not make a gift of community personal property, or dispose of community personal property for less than fair and reasonable value, without the written consent of the other spouse." The nine community property states do not all handle this the same way, so it is a question to ask locally rather than to assume.
When the claim is contested. If two people plausibly claim the same proceeds, an insurer will commonly file an interpleader action, deposit the money with a court and let the claimants litigate it between themselves. There is a federal statute written for exactly this situation: 28 U.S.C. section 1335 gives the district courts jurisdiction over an interpleader action by a corporation "having issued a note, bond, certificate, policy of insurance, or other instrument" worth $500 or more where "two or more adverse claimants, of diverse citizenship," claim the money, provided the insurer pays it into the registry of the court. That is the mechanism by which a stale designation becomes a lawsuit rather than a check. Separately, slayer statutes bar a person who killed the insured from collecting. The Supreme Court observed in Egelhoff that such statutes "have been adopted by nearly every State" and that the principle underlying them "is well established in the law."