The patent applicant writes an individual, but can I invoice the company name when invoicing? Or must it be the applicant's name?

First, there is something wrong with your application. If the inventor is an invention made by taking advantage of the conditions of the unit and belongs to a service invention, the inventor may be an individual, but if the applicant needs a unit, it will be authorized to the unit;

If you do it with your own resources, the right belongs to you completely, and you can also invoice in the name of the company. This situation requires prior agreement, that is, the company authorizes individuals to apply and give up patent ownership.