Apologies if I've missed the point of the discussion, but Luna Azure is the name of the restaurant in the novel. The one where the hits occur, not where Clemenza has lunch.
You are correct. Luna Azure is the name of the restaurant in the novel where Michael shoots Solozzo.
Signor Vitelli's post was talking about the film version. It was filmed in Louis Italian American Restaurant. The film version did not change the name of the restaurant to match the name of the restaurant in the novel.
The deleted scene of Clemenza having lunch and picking up the cannoli's were filmed at a Luna Restaurant. I found some information online that it was located on Mulberry St. Not sure how true that is but that is what I read.
