How do you determine the insurer that issued a life insurance policy?

You could look at bank statements to see if there are premiums that come out regularly. Ask the deceased's friends, since agents are usually recommended. Without the company name there is not much one can do except start calling. There are services that you can pay for(at a hefty premium) to locate your policy. They are called Heir Locators. They charge a percent of the policy.

Since there is no company that links all the Life Insurance companies together, it is hard to find without a company name.