homeowners insurance new mexico

Is it necessary to change home insurance if you rent your house out?
We are moving to New Mexico this June and the rent of the house we have. I know as a renter, you can get insurance above and beyond their owners to protect their personal belongings, but I wonder if we have to change our home owners insurance for tenants. Does anyone know, or know who would?? Thanks so much!
I rent a house and homeowner's insurance does not cover our personal possessions. The owner made it clear that we had to get renter's insurance if wanted our objects personal coverage.