If you are on the deed OR you have received this property by devise, you will be able to fill our a name change form and file it with Harris County Appraisal District. If your name is on the "recorded" deed, attach a copy of the recorded deed to the name change form.
If you have inherited the property and the will has been probated, it is easier to hand carry that probated will into Harris County Appraisal District's office to finalize the addition of your name. They will be able to see the probated will on the County records.
I am assuming you are referring to homeowners insurance. Homeowners insurance is available to owners at a better annual rate than non-homeowners insurance.