Can a sign name be given by someone non-Deaf if they still primarily use ASL?

First of all, I hope it’s okay to ask about a fictional scenario. I’m in the process of planning a story, and one of the characters is canonically nonverbal (due to a vocal cord injury as a child). Because of this, he knows how to speak but cannot, and primarily uses ASL to communicate. He is able to hear.

Would it be wrong or offensive to have the character give and use sign names for the people in his life, like his parents and close friends? Appreciate any insight.