It's fairly obvious that one of the valuable assets of almost any business is the business name - and all the market presence, familiarity, and good will associated with it.
So, how does that name get transferred to the new owner?
Let's assume that the buyer is forming a new corporate entity (a corporation or limited liability company "LLC") or is operating as a sole proprietorship. In many cases, the prior owner will need to file an official abandonment of the fictitious business name "FBN" (commonly called the "dba", for "doing business as") and the new owner will need to file an application to assume that name. This application is filed with the county where the business is located, and then a notice of the filing must be published in a legal "newspaper of record" within that county.
The new owner will need to establish identity and authority. If the new owner initially registers the FBN in an individual name, all that is needed is to establish personal identity. If registered as a corporate entity (Inc. or LLC) or a transfer it to a corporate entity, the new owner will need to establish that the entity is in "good standing" and that the individual has the authority to act on its behalf.
In any event, while I do not provide legal advice (I'm a member of the New Jersey Bar, not California), in my experience as a business owner, I would ALWAYS include my corporate name on every form, document, contract, receipt, and correspondence - regardless of having a fictitious name, so that there could be absolutely no misunderstanding that I am operating as a corporation or limited liability company and not as an individual. And, I would sign everything in my corporate capacity, not as an individual. (E.g., "John Doe, Managing Member of Doe Enterprises, LLC, dba 'Obadiah's Sub Shop' ".)
Alternatively, the new owner can establish their corporation or LLC with the name of the business, such as "Obadiah s Sub Shop, LLC" and always show the "Inc." "Corp.", or "LLC" as part of the name. Then there would be no need to file a fictitious name statement at all. (If the business name is part of the seller s corporate name, then the seller will need to file a simple application to change the name of the selling corporation to something else, e.g., "Obadiah's Old Business Entity, LLC".)
I suggest that business buyers always discuss this with a competent experienced business attorney so that the "corporate shield protections against personal liability are preserved, regardless of whether or not the business registers a fictitious name statement. Every transaction is different and every business unique, so sound legal advice is essential.