This isn't an area in which I claim any expertise, but in the event of a loss, the policy will pay to the named insured. I am aware that if the insured is a named individual rather than the Trust even though title to the property is in the name of the Trust, and say John Doe is injured on the property, John Doe will be paid by the insurer on behalf of the individual but may still be able to go after the Trust since it is the owner of the property.
The grantors/settlers of inter vivos (grantor or revocable) trusts do not usually list personalty transferred to the trust, and I doubt the mortgagee is taking a security interest in contents. If the grantors of the Trust are not co-borrowers, I believe the contents will be deemed to be owned by the Trust and insured, but this is a question that the grantors/trustees should put to their insurance agent.