Dear [Name],
I am writing to apologize for misnaming you. It was wrong of me to do so and I am deeply sorry for my mistake.
I understand that words are powerful and that misnaming someone can be hurtful. It was never my intention to cause you any distress and I regret that I did. I understand that my mistake was insensitive and I take full responsibility for it.
I understand that I have caused you pain and I am sorry for that. I will be more mindful and careful in the future and make sure that I use the right words when referring to you or anyone else.
I would like to take this opportunity to apologize to you in person. I would also like to offer to make it up to you in any way I can. I understand that this may not be enough to make up for my mistake, but I hope that you can forgive me.
Once again, I apologize for misnaming you and I hope that you can accept my apology.
Sincerely,
[Your Name]