Criminal Sentence 131: Big name or big store?

From something I recently edited:

"The big name stores don’t attract the same people."

As I noted in the title of this post, are we talking about a big name or a big store? A hyphen will clarify things: "big-name stores."

If you have two words that modify one thing, then a hyphen helps link them:

high-wire act
low-maintenance haircut
well-written sentence