Can I apply for a patent for the company name?

No, the so-called patent is an invention-creation, that is, an invention, utility model or design applies to the State Patent Office for a patent, and after being examined and approved according to law, the patent applicant is granted the exclusive right to enjoy the invention-creation within a specified time. The company name is not a specific invention, so you can't apply for a patent. But the "Haihui" you mentioned belongs to the enterprise name. According to the "Regulations on the Administration of Enterprise Registration", after the enterprise name is registered by the industrial and commercial department, it naturally enjoys the exclusive right of the name in the county-level area, and others can be prohibited from using it, but enterprises outside the county (city, district) cannot be prohibited from continuing to use it. If you want to enjoy the exclusive right nationwide, you can also apply for a service trademark in accordance with the provisions of the Trademark Law.