Yes, definitely you need to have a legit license to start an ecommerce business.
Doesn’t matter, if you own a digital business (or) a physical business, every business owner needs a license from the state/central government to continue the business.
License is the only thing that makes the business legit, legal, and real in the eyes of the government, and if you’re running an ecommerce business without licensing and permissions, then you might end up paying penalties and get yourself suspended for not complying with the business norms.