You should check the jurisdiction's municipal code. Per the IRC, the jurisdiction is required to state in the statutes (municipal code) if construction documents are required to be prepared by a licensed design professional, otherwise, you could prepare the drawings yourself.
Technically the permit is owned by the property owner. But the jurisdiction may have a specific process to add a new GC which often includes providing a letter from the property owner along with the GC information - just be sure the GC is licensed and has current insurance.
Hola, my name is Kim and I work for a permit expediting company in Colorado. I previously worked as a Senior Permit Tech in a Denver suburb and now I'm on the other side of the fence! Looking forward to discussing hot topics in the world of permitting!