I'm not sure this is Linkedin's problem to solve. They are just a directory.

I suppose they could add a phishing warning for messages sent on LinkedIn, but really it's an education problem, teaching people to identify what phishing emails look like and how to avoid them. This is a problem I've been working on since at least 2003, when we realized that the best way to prevent eBay account takeovers was teaching people what phishing is. We also identified that education is the hardest solution to achieve.

It's ironic that the security professionals are the ones hiding their identity, given that they are the best prepared to identify and avoid phishing emails.