You can check the WebClient
documentation for a C# sample that adds a User-Agent to your WebClient
and here for a sample for Windows Phone.
This is the sample for C#:
WebClient client = new WebClient ();
// Add a user agent header in case the
// requested URI contains a query.
client.Headers.Add ("user-agent", "Mozilla/4.0 (compatible; MSIE 6.0; " +
"Windows NT 5.2; .NET CLR 1.0.3705;)");
This is a sample for Windows Phone (Silverlight):
request.Headers["UserAgent"] = "appname";
// OR
request.UserAgent = "appname";