Letters can be very cathartic; it depends on what you want to accomplish. If the idea is to make someone aware of a wrong they have committed, they probably know it’s you, anyway. The letter gives them the opportunity to right the wrong, if they respond appropriately.
Sometimes a letter is intended not to elicit an apology but just to vent. In that case, I would leave my name off probably. Other times, it is crucial for the person to know who is sending the letter, and hopefully they will be mekabeil the mussar.
And SOMETIMES it is good to write everything that comes to mind, vent like crazy, and then tear up that letter and send a calmer one.