Legal Question in Business Law in California

Your question is somewhat indefinite in that it doesn't state whether the complaint is one to be made in the courts, to the BBB, or directly to the owners of the business (or whatever). You also don't say whether the customer is asking for the names of the shareholders of a corporation, the partners of a partnership, or whatever.

My general feeling is that a business has a legal duty to reveal its true name to its customers. Then, for example, if the business is a corporation, the complaining customer will be able to go to the secretary of State and obtain the names and addresses of the officers, directors and registered agent for the service of process.

You need to be sure your business has complied with the laws requiring county registration of any "fictitious" business name is uses. For example, a sole proprietorship calling itself "Acme Plumbing Supply" would have to file that name with the county clerk and publish a notice in a local newspaper of general circulation.

Finally, in general I think it is unwise and unethical for a business to conceal facts about its owners from its customers. If it is a corporation with 50+ shareholders, that's another matter, but if it is a partnership, proprietorship, or LLC or corporation with relatively few owners, in general a customer should be furnished this information. There may be exceptions, but not usually.