Whether your home was damaged by something as wild as a tornado or as commonplace as an overflowing washing machine, your insurer may suggest a contractor to do the repairs. They may call them "preferred" but that doesn't mean you're forced to hire them to work on your home. It's generally up to you to pick who's going to do the actual work. Your insurer should cover the bill for your selected professional, (above your deductible and up to policy limits) as long as that professional has specified in advance the materials and tasks that need to be done and priced the work fairly.
United Policyholders offers many resources to help you navigate home damage repair claims and resolve conflicts that may arise. You'll find sample repair/rebuilding scopes and estimates, tips and guides in theProperty Damage section of our Claim Help Library.
Occasionally an insurer will exercise an option that's in most property policies that allows them to "elect to repair" (take charge of the repairs). You can read more about that scenario in a recent entry on the Property Insurance Coverage Law Blog.
Laws and policy language vary state by state, but if you pick a reputable and qualified repair professional who presents a detailed estimate that's in the right price range for the job and you "Speak UP", your insurer should pick up the tab.