As a general rule, this is not permitted due to the possibility of infringement of the standards for restrictions on side jobs (When a side job uses the employee's position at the company). However, if there is a request from the side business employer, and it does not fall under the restriction criteria, only the name of the company, department, and position to which you are currently attached will be permitted.
*Regardless of whether there is a request from the side business employer, if it can be objectively determined that the side business employer actively expects to attract customers or promote sales by using the company name, or if it poses a risk to the company's brand, reputation, etc., usage will not be allowed.