Inventor or designer refers to the person who invented or designed the method or product, and must be a natural person, not an invention of a certain unit. So in the inventor column, you have to sign your personal name. Inventors can be several people, but not two.
As well as the applicant and the patentee, if it is a service invention, the signature is the unit; If it is a non-service invention, you can sign your own name.
There is no case where both units and individuals sign at the same time.