This doesn't give the person who receives this letter enough information to do anything.
Dear Customer Service:
My name is Ebony Brown, and I have two accounts with you. The account number are *** and ***. I would like to close both of these accounts. [If there is any balance, you need to tell them how to handle it - do you want a check mailed to you, etc.?] If you have any questions, please contact me at ***-***-*** (this is where you should put your phone numer or your e-mail address.) Please let me know if I need to provide any other information.
Sinerely,
Ebony Brown