Does it matter if I help my friend name the supervisor and start my own company?

It doesn't matter.

The nominal supervisor of a company is not necessarily the legal representative of the company. As a supervisor in this company, he can supervise the operation of the company, so he can register himself as a legal person.

Supervisors of state-owned enterprises may not hold positions in other companies.

According to Article 69 of the Company Law, the chairman, vice-chairman, directors and senior managers of a wholly state-owned company shall not hold part-time jobs in other limited liability companies, joint stock limited companies or other economic organizations without the consent of the state-owned assets supervision and administration institution.

Precautions:

Nominal supervisors generally have no influence on themselves. Generally speaking, supervisors do not bear general legal responsibilities, but they do under certain circumstances. It is the company's behavior not to assume debts. For example, the nominal supervisor is at fault and needs to bear legal responsibility. Such a nominal supervisor is not recognized by law.