You lose anonimity in a very short time if you either:
1- Use the new "anonymous" sim card with a phone you already own and used with other sim card (IMEI matching).
2- Use a new phone with the new sim card but let it connect through your home WiFi network (IP tracking).
3- Use a new sim card and a new phone, but carry the new phone around with your main phone so that they find your second phone and number just by looking in the carrier(s) database(s) if there are any matches to the tower areas the first phone connects to.
1- Use the new "anonymous" sim card with a phone you already own and used with other sim card (IMEI matching).
2- Use a new phone with the new sim card but let it connect through your home WiFi network (IP tracking).
3- Use a new sim card and a new phone, but carry the new phone around with your main phone so that they find your second phone and number just by looking in the carrier(s) database(s) if there are any matches to the tower areas the first phone connects to.