How can I get a big-name entrepreneur to publicly endorse my product / service?

Big-name entrepreneurs get asked to invest / endorse / recommend products and services all the time.  So if you want to stand out, you need to set yourself apart from the rest.  Do not ask for a recommendation or endorsement. Instead, find some commonality between yourself and the entrepreneur and provide some value before asking for something in return.  Perhaps find a recent  article they’ve written and engage in discussion, or find a way to add value to one of the entrepreneur’s existing ventures or initiatives.  After you have a discussion where you have provided some type of value, then you can suggest that the entrepreneur take a look at your product and give you an endorsement if they find value in it.