The answer here is going to depend on the laws of your state and the policies of the insurance company. The lack of a named beneficiary introduces a wrinkle in the decision if you live in a state that does not recognize domestic partnerships, but if the insurance company permits them, then the state laws are a moot point. Even having a policy without a named beneficiary is a bit unusual, since most insurers will want you to name at least one person to inherit the proceeds of the policy.
It would be better to name your domestic partner as a beneficiary. Since the owner of the policy can name any beneficiaries they choose, being listed would eliminate any conflicts over domestic partnerships. Without that, any close relative of the deceased could challenge the payout of the policy and might be able to completely exclude your domestic partner from any portion of the settlement. It only takes a few minutes to update a life insurance policy, and you should always review you beneficiaries any time you have a major life-changing event, such as becoming domestic partners.
In most circumstances, a policy with no named beneficiaries will pay out to the first closest relative of the deceased. If domestic partnerships and common law marriage are recognized in your state, then your domestic partner is the automatic recipient, but if your state does not recognize domestic partnerships, your death could result in a legal battle over the proceeds and there is no way to determine how the case would turn out.
It is the law in your location, not the way life insurance works that is the determining factor here. If the law does not provide for domestic partnerships and the insurance does, your partner will receive the settlement, but if neither the law nor the insurance company has taken this step yet, then only an attorney can accurately predict how the situation will end.