Due to the amount of people requesting their previous names to be deleted, I have made it possible to remove your own. All you need to do is have a confirmed account. Once you have that you can go to your profile and your old names have a cross next to them should you wish to remove them
You can confirm your account here. You must be in a clan to do this. If you want your previous names removed and you're not in a clan or able to confirm, then just submit a RSN change here including your RSN as both your old & new rsn and include a comment asking for your names to be removed.