While a plumber who is properly licensed by the TSBPE can work anywhere in Texas with his license, most cities require that contractors be registered with them in order to pull permits and schedule inspections in their city.
It doesn't matter if the plumber operates his own company or works under another, that company must be properly registered with every city in its service area.
Many city websites host portals where residents can look up contractors who are registered in their city and keep tabs on permits/inspections. For instance, Frisco, Plano, and Prosper all use the eTRAKiT platform for this purpose.
At the end of the day, if a contractor pulls a permit and schedules an inspection with your city in order to perform work at your home, you can rest assured that this contractor is registered with the city and in good standing.
If a contractor is performing a large installation such as for a water heater, remodel, or renovation at your home and does not talk with you about permits and the inspection process, this is a red flag. The city permitting and inspection system is set up so that homeowners like you can be protected from sub-par construction practices that violate code requirements.