You might take a look to the C# sample called NetRadio - it covers exactly what you are looking for.
To obtain the station name you can call the following:
_stream = Bass.BASS_StreamCreateURL(_url, 0, BASSFlag.BASS_STREAM_STATUS, yourStreamCreateProc, IntPtr.Zero);
string[] icys = Bass.BASS_ChannelGetTagsICY(_stream);