Electronic Frontier Foundation, in a story by Jeremy Malcolm, report that domain name registration companies are asking ICANN (now meeting in Dublin, Ireland) for forbearance in publishing personal information from domain name owners, in order to comply with data privacy laws in many countries. The story is here.
ICANN does allow currently Private/Proxy registration services, as explained here. BlueHost, for example, explains its policy here.
But the EFF story links to an earlier story about a proposal to by ICANN to disallow private registration for domains intended for commercial purposes. Large entertainment companies may seek this change to make it easier to pursue copyright and trademark claims.
Private registration is intended in part to protect individual domain owners from possible trolling or stalking, possibly from people with unusual sensitivities to usually innocuous topics (like vegan diets). The risk can be mitigated, however, by taking out a land-address box with a UPS store or similar service.
It appears from my own WHOIS check that my two Wordpress domains at BlueHost are private.