Assuming that both parties have not signed any legal documents about trademarks before, it depends on who owns the trademarks. Trademarks registered in the name of the parent company belong to the parent company, and trademarks registered in the name of the subsidiary company belong to the subsidiary company.

Hypothesis 2: If the parent company has transferred the trademark ownership to the subsidiary company.

If the ownership has been transferred, it belongs to the subsidiary.

Hypothesis 3: The trademark is jointly owned by both parties. After leaving the parent company, the subsidiary believes that the original parent company's continued use of the original trademark has caused damage to it. What should a subsidiary do? If the trademark is owned by both parties, both parties have the right to use the trademark, and the subsidiary and the parent company can negotiate and transfer the ownership of the trademark.