i think its appalling that mumsnet are allowing them to do this, it is one thing to post on a site that generally only mums use and small compared to some, but quite another to print in a national newspaper , also your site name could be a name that your friends know in a general sense as a nickname, yes vyou can change it but it might be too late now the dm may have already used it.
I am really suprised that mumsnet hasnt told them at least not to use the real nicknames!