could you please help me to understand the meaning of "O's" in such names as "Nancy O's restaurant", "George O's bar"... etc. Is there some special meaning, is it translatable? Thank you a lot!
This is not a standard pattern.
In the case of Nancy O's restaurant it is "The restaurant of Nancy O". As far as I can tell "Nancy O" is a fictitious name. But it could suggest an Irish name, as many Irish names such as "O'Brian" or "O'Leary" where the "Ó" means "descendant" in Irish Gaelic.
I can't find "George O's bar". It might be another bar named after a person with an Irish name, or it could be Georges's restaurant in Waco, which serves a drink called "Big Os". That is short for Big Oranges.
Other than that I don't see O's in many other bar names. It is, part of the name, and so not translatable.