I'm hardly surprised that the Sun has stooped to this kind of journalism, after its sister paper (and itself no doubt) have not refrained themselves from tapping-up the phones of celebrities, public figures, murderers and the murdered. Its thoroughly deplorable and should be stopped.
An injunction would stop the paper from revealing the name but they can cost tens of thousands of pounds and only our womanising footballers and celebrities have that kind of money to throw around.
Hopefully common sense, and/or public condemnation, will prevail and they'll leave this unfortunate person alone to spend time with their child, instead of worrying about this witchhunt.