Can you own a business in Thailand with a DTV visa?

First of all: unless you are US American or open a very special business via BOI, you cannot fully „own“ any business. You can own a 49% share in a business with Thai partners holding the rest. There are ways (preferential shares) to still remain in control as a minority shareholder - though gray area. Having said that: in order to legally work even for your (co-) owned company, you would need to switch to a business visa and get a work permit. But you would only get a work permit for „your“ company, if that company has 2 million baht of nominal capital and 4 Thai employees hired for every foreigner with a work permit (including yourself).

You can own a business with any visa or without a visa. But you cannot do any work at this business without a work permit and visa that allows work.

The DTV is strictly work prohibited and you cannot work for a Thai company, work for Thai customers, or get a work permit on DTV.