Should we get another company registration for new branches open?
No. In India, there is no need to get a branch registered as a new company. As per the requirement, you can simply set-up a brand and commence the business in same company name.
Although there is no requirement for new company registration, you may require to obtain tax registration, like GST registration or other local registrations, like Shop & Establishment and PT Registration for the branch office.
Further, the branch office address must be updated as and where required.