Back in the late '60s when I was restoring a Model A that was registered in California by engine number, they had a form for engine change that required that you notify them within 10 days of changing the engine. The registration was by engine serial number, (although the number was stamped in other places on the truck.) This was before VIN's were widely used on new vehicles. Since the truck wasn't on the road, I figured that they'd waive the 10 day requirement, but I got a stickler at DMV. They wanted to fine me for not reporting the change within that time. I left and went back with a "corrected" form, and got the truck registered. They also required a "certificate of non-operation" with info like your neighbor's name and address and a local gas station. Like they were going to check.
Hopefully Texas isn't as bad as California was back then.