You can’t delete a Bungie profile (Bungie doesnt have accounts). The best you can do is link a new/alt account to this profile if you no longer want to use it. If you need to change the linked account on the profile, then you need to link a second account to the profile so that you can unlink the current linked account then link the new account (as each profile must have 1 account linked to it, otherwise it becomes orphaned & cannot be retrieved in the future).

Hey there! Unfortunately there is no way to delete a Bungie account. You can however unlink all accounts from this profile and link them to the new one. All emblems tied to your current profile do not carry over to the new one.