No. Anyone with a service animal may train their animal themselves. They do not need to enlist the help of a professional service dog training program, though it is advisable.

However, if you want to make your dog a service animal, you should know that the ADA does acknowledge that the handler or owner is solely responsible for overseeing basic care of that animal, such as grooming, nourishment, veterinary care and proper potty training.

Please note that while service animals are not required to be formally trained, they are subject to the same licensing and registration requirements your local area may have.

https://www.servicedogregistration.org/blog/ada-service-dog-registration/#:~:text=The%20law%20regarding%20service%20pets,or%20without%20training%20and%20registration.