[simne]

This is timebomb. Information saved in search engines, etc, any time could appear again, and will look hugely contradict with current site activity.

I think, better to register/buy other domain, with different name.

If you have much money, also could for convenience of customers, make dedicated site with old name, where write on very beginning of main page something like "this site dedicated to memory of good person, but if you looking for ...co, redirect here (link)", but this is terrible solution, considering people could enter to buy something and they will first see negative information. But for some things this is not so important.