Legal Question in Business Law in California

First off, changing the name of the subsidiary is totally irrelevant. Next, the whole point of a parent-subsidiary structure is to insulate the parent company from any liability for the subsidiary's operations, regardless of whether the parent keeps or sells the subsidiary. The parent is merely a shareholder of the subsidiary, and the whole point of incorporation is to insulate the shareholders from personal liability for the corporation. The exception is that if the parent runs the subsidiary not as a separate and independent corporation, but more as a mere division of the parent, a plaintiff can try to "pierce the corporate veil" the same as if an individual sets up a corporation and then runs it like a sole proprietorship without separate and distinct existence. As for the impact of the sale, IF liability arose before the sale, and IF the plaintiff has grounds to pierce the parent-subsidiary veil, OR the subsidiary itself was not sold, but only the assets, leaving the subsidiary as an empty shell, the original parent would be a proper defendant. In many cases new parent B could also be sued. That frequently happens and raises issues of how A and B agreed to allocate responsibility for past liabilities (an essential term of the sale of a subsidiary) and whether the sale was structured as a sale of assets or a sale of all the shares of the subsidiary as a going concern.