I was advised by a few recruiters to remove all PII from my resume but my email, both for privacy reasons and because it's better to funnel all offers to the same location. I still keep my phone number on there, but if someone really wants my data, it's remarkably easy to find, so I am not really doing much by just removing it from my resume. Oddly, I've had a few people actually try to find more PII on me and fail miserably. They claimed to be good at it, and should have known enough to find at least my legal name with ease. Used to be able to find old AIM conversations of mine if you knew what to search for (or got lucky).