string s = @"sdwqdhwqkghkg321 dsw wq dwq { name:""我dni单位"",dwqdwquidwq";
            System.Text.RegularExpressions.Regex reg = new System.Text.RegularExpressions.Regex(@"name:""(?<value>\w*\W*)""");            
            System.Text.RegularExpressions.Match m = reg.Match(s);
            MessageBox.Show(m.Groups["value"].Value);

------解决方案--------------------

C# code

string str = @"sdwqdhwqkghkg321 dsw wq dwq { name:""我dni单位"",dwqdwquidwq";
Regex re = new Regex(@"(?is)(?<=name:"")[^""]+(?="")", RegexOptions.None);
MatchCollection mc = re.Matches(str);
foreach (Match ma in mc)
{
  //ma.Value就是你要的值
}