Article before restaurant names

Hi,

1) Let us make a fictitious business name for the purpose of asking a question: XXX's Chinese Take-Out -- let us pretend that is what was on its sign but is not there anymore. Can I say this? I am going to attach what I think is the generic word "restaurant" at the end for the purpose of asking this question.

There used to be a XXX's Chinese Take-Out restaurant in this street in 1980s but it is not there anymore.
Or
2) Now, if there is one now, can I say this?

Where is the XXX's Chinese Take-Out restaurant?
Where is XXX's Chinese Take-Out?

I think this is not correct unless there happen to be two or more restaurant with the name "XXX's Chinese Take-Out. Do you agree?

Where is a XXX's Chinese Take-Out restaurant?