Must the subsidiary company share the same name as its parent company?

The name of the company is your decision, and it need not be the same as the parent company. However, the names of companies are subject to review by the authorities if it contains sensitive words, or if the name is similar to an existing company.

Suggested Readings

Are there reasons for a delay in name reservation by ACRA? What are the requirements for shareholders of a subsidiary company? Can a Singapore subsidiary hire foreign employees? Can all the directors in the subsidiary company be foreign?