The easiest way to get the name of the Current Network Operator to which the Android phone is currently connected is to get hold of the android.telephony.TelephonyManager and get it from there:

TelephonyManager telephonyManager =((TelephonyManager) Context.getSystemService(Context.TELEPHONY_SERVICE));
String operatorName = telephonyManager.getNetworkOperatorName();

similarly the sim operator can be retrieved by using:

String operatorName = telephonyManager.getSimOperatorName();