Configuring a Microsoft SQL server for usage with Oracles SQLDeveloper.app isn't quite as simple as it could be, the login and authentication when using Windows Authentication doesn't seem to work. Specifically, it doesn't look like the "Windows Domain Name" parameter is picked up from the configuration.
Instead, amend the entries in the Port field instead and suffix them with the domain= parameter.
In the example here, the Port field has the value; 1433;instance=MSSQLSERVER01;domain=DOMAIN;appName=MadeUp;
Where; instance=MSSQLSERVER01 is the instance name of the SQL server (this could be optional depending on your installation). domain=DOMAIN is the login domain of your windows user account. If I were logging into this server via RDP I'd be logging in as DOMAIN\siftah