Keeping the patent in your name and that of the company owner would create a joint ownership allowing either of you to exploit the patent. I am assuming that the manufacturer is the company that is owned by the company owner. If you did not assign your rights to the company, then you would have the right to sell rights to the patent to other companies, or to go into competition against the company.
Generally patent ownership is a question of state law and you should consult an attorney versed in the state where the verbal contract was executed. It seems that the company agrees that you are an inventor. If that is in question, then they could claim that you are not actually an inventor and have no ownership claim. Absent a written contract, the issue may well be determined as to who is actually the inventor. If you are not an inventor, then you would not have an interest in the patent rights. You state that you were commissioned as a designer. The level of contribution of your efforts to the actual claims of the patent might need to be determined. If you were merely creating a design of a product based on the explicit directions of the company, then you might not actually be an inventor. On the other hand, if you were only given very general directions and you created a product that was mostly dependent upon your efforts, then you may well be either the inventor, or one of the inventors and have an interest in the ownership of any patent that might issue.
Unless you and the company owner are able to jointly agree upon the question of ownership and/or inventorship, then that question may not be able to answered, until a patent application is filed and claims allowed. At that time, the question of inventorship and ownership might be determined. Of course someone will need to pay the costs of the patent application and prosecution first.