Roblox allows all users to change their Roblox account's display name in the account settings without spending a dime. Here's how to do it.

To get or change a Roblox Display Name, you should first log in to your Account Info page under Settings, then select the edit button next to the Display Name entry above your Username.

You won't find any automated way to delete a Roblox account on its website. Use one of the 3 methods listed in the post to delete Roblox.