The Uri should be your Cluster Name, not Username, like:
var hadoop = Hadoop.Connect(new Uri("https://clustername.azurehdinsight.net"), "username", "password");
var config = new HadoopJobConfiguration();
config.InputPath = "input/CodeFiles";
config.OutputFolder = "output/CodeFiles";
var result = hadoop.MapReduceJob.ExecuteJob<NamespaceCounterJob>();
The cluster name is shown at the top of the detail page in the Azure portal for your cluster. Also, you don't need to enable RDP to use this method, it's actually the username set for "Hadoop Services" in the configuration tab of the cluster. Launching a job in this manner makes use of the WebHCat/Templeton endpoint, so RDP is not required.
I hope this helps you :)