When Bran arrived back to Winterfell, obviously every time he met another member of his family they hugged him and were very happy to see him. He never kept it a secret that
he was actually not Bran, and that Bran is dead.
Yet, everyone kept treating him as a Stark family member.
He was there in every meeting and council and also in a closed family-member-only conversation, even though he was actually a stranger.
Why would they let the Three-Eyed Raven keep Bran's status as a part of a big house family, including him in meetings of the highest ranks, and of course, keep showing affection as you would to a brother?