Welcome to the wonderful world of boats in Mo. There are the rules, and then there is reality.
First off, if it is not self powered; paddles, it has to be registered and display the numbers properly. A trolling motor does not have to be registered, but it does not fit the self powered requirement, so the boat has to be. If you have a battery to run the motor, you have to have a fire bottle because a battery is a flammable liquid according to the WP. That is the simple plain part of the equation. From there on it gets strange.
Yes, there is a form to register a boat. When you ask your liscence office about it, they will laugh at you, even tho Jeff City tells you it exists. If you do get the form from the liscence office, the WP will tell you they don't know what you are talking about when you go see them. If by chance you get past them and go back to the liscence office, they will require tax records since the boat was new or things stop there.
We just went thru this on two boats. One was a plastic 10 foot pond or lake boat. In the end, I sent it out of state and had it registered there. Once I had paper from the other state, then things were simple. The second one was crazy. My fathers boss died of cancer. He gave the boat stored in the barn at the farm to my dad. According to the law, when he died, his son had 1 year to change everything over. They did not get the boat transfered during that time period. Dad finally went to get the boat titled in his name and they said no. After the year is over, no one can register that boat but the dead man. They actually said that digging him up and getting him to sign the papers was the only way it could be done. After two trips to Jeff City, several to the water patrol, several to the liscence office, and hours on the phone, a congressman got us a title somehow. It took about 18 months before the boat was legal so it could be used.
I have a little plastic boat out in the yard that has a fire bottle and lights so it is legal to use a trolling motor on it.
My neighbor just gave a 18 foot inboard outboard V8 former water patrol boat away. The title was messed up, and I would not take it for free because of that. Neither would my dad or anyone else that has ever gone thru it around here.
Good luck!