The official stance on the three default groups in Google Contacts (Family, Friends and Coworkers) is that they cannot be renamed nor can they be removed.
Now I am not going to argue this point, mostly because, unlike Google Alphabet, I am not worth some half a trillion dollars (okay, they are worth significantly more than that – keep in mind when this was written!).
What I will say is that, if you have been using anyone’s service long enough, you will find it possible to be an edge case, where the regular rules don’t apply, and suddenly you have figured out how to get around the official stance, and naturally, no one else has come across the exact some problem. Luckily, there is a way to solve this particular issue. At least, until they close the loophole.