Instead of liquidating the East India Trading Company, say the British keep it like the Hudson's Bay Company. Would the EITC than become a company dealing in silverware, tea, porcelain, condiments, dyes, and fashion (primarily silk)?
I'd argue it was more an odd appendage of the British government than a real business. Its power and wealth came from it's administrative duties and by the time it was dissolved those had already been taken over by the government directly and it had really ceased to exist in all but name. I doubt it would continue in any form even it it wasn't dissolved but any EITC that did survive into the 20th century would have nothing in common except the name. Also I think their history is far far too bloody to make a good modern brand for consumer goods.