Yes obviously. If you are selling anything that has your name then it must be registered. Period. As it will be designated to your name, and if you don't do it then your name will be of no use. If you were selling on any platform like I am doing it through Walmart: https://www.reecoupons.com/view/walmart I don't need to register as I am using Walmart's name.
Business registration is required anyway to start a business in India. However, choosing an appropriate business structure is vital aspect not to miss, alike targeting market. For a small business, registering a company may be costly in terms of compliances. So, you can get in touch with a professional to guide to establish your business. You can get in touch with our experts at http://www.legalwiz.in.
No, It is not necessary to register your newly started company, but my suggestion is that you do that as early as possible. Like the company I have https://www.pennysaviour.com/ is not registered yet but surely going to register it soon.