Generally yes, both with an existing policy (unless you have given up that right, perhaps in connection with a divorce decree) and a new policy.

It is not necessary for the beneficiary to have an insurable interest in the life of the insured. For example, you may wish to buy a life insurance policy naming your college or a buddy as beneficiary. (Of course, if your buddy is a known mob "hit man", the life insurance company may not want to issue a new policy.)

Where a person ostensibly buys a policy on his own life, names an appropriate beneficiary, and then promptly changes the beneficiary and "assigns" the policy to someone without an insurable interest, there is always the possibility that it was part of a scheme to avoid the insurable interest rules, which may render the policy voidable.