If you bring the head of Alexandar to the Sallow Man, you lose your Noble tag as the Red Prince.

There is no dialog option to decline having him add a new tag, so I believe it isn't meant to be deleting an existing tag.

Technically, you could put the head on the alter, go inside, then attack the Sallow Man rather than talk to him and not have this issue. Either way, for the Red Prince especially, losing the Noble tag makes no sense.

This all happens before the point where you are asked to swear to the god king, so it's not like you are going out of your way to help the bad guys. I was going to kill him either way, Alex that is, and just wanted to get access to kill all the black ring too, and ses out what they have going on before fighting, so I brought the head on over. Then I ate the Sallow Man's head (using Fane's mask), and consumed his soul afterwards... I did want to eat Alex's head myself, but I figured eating the one who just ate him is close enough.

at the moment you are given the option to claim the reward

if you choose to leave, the swallow man is not going to change the tag and you can go ahead with your dialogue as if you had received the "reward"

i suck at englishman just pick the other option and thats it