If you are using the streamlined 203(K) you are allowed to get estimates from each of the professionals that you intend to use. You must provide the bank with a written cost estimate(s) and references from a duly licensed and bonded contractor(s) for each specialized repair or improvement. For example an estimate from the roofing contractor or an estimate from the contractor to replace windows.
Otherwise HUD does not have an approved contractors list, however, it's nice to hire a contractor that has done 203(K) work before, but any contractor you choose must be licensed and bonded and must be willing to complete the work under the HUD payment guidelines. The contractor should be willing to get paid in stages, for example, as construction progresses, funds are released after the work is inspected by a HUD-approved inspector. A maximum of four draw inspections plus a final inspection are allowed.