Yes, one can use the same brand name if your activity is different.
The trademark ministry has provided 45 different classes for different products and services. So, one can take registration of similar brand name in a different class as per the business activity, even if someone has already registered its trademark in different category. But before starting a business one must check the availability of brand to avoid any discrepancy at later stage. One can have a better idea about trademark classes through our blog How Should I Pick Appropriate Class for Trademark Registration?