Does homeowners insurance cover others peoples belonging in the home if you are not on the policy?

Normally the policies are written in such a way as to cover "the house located at (address) and its contents (up to some dollar amount)", not "(specific person)'s belongings", so there's no need for anyone to be specifically listed on the policy. If the items in question were in the insured dwelling, and they were damaged due to something the policy covers, they should be covered.

If there's any question in your mind about what's covered and what isn't, call your insurance agent and ask. You don't want to assume that your friend's $50,000 stamp collection you're storing in your garage is covered and then find out that it wasn't because you didn't specifically declare it or something.