Name with a person's name or part of a person's name

Hi. Can you tell me why it is as it is as I think it is?

Most of the time when we are dealing with the name of a business that has a person name or part of the person's name in it, the article seems not be used.

eg,
We went to John Doe's Restaurant for a light meal.

Then, I think I saw the articles being used for a name like this. Why is that?

We went to the Doe's Website for his above-normal coverage of the event that occurred yesterday.

If the above sentence doesn't require an article, could you come up with a case that will require one and has part of a person (or looks to be part of a person's name) in it?