TikTok doesn't allow its users to have empty nicknames. If you try to set your nickname to an empty string by using space characters, it will complain: "This nickname is not allowed."
To get an empty nickname, you can just use the invisible U+FFFC OBJECT REPLACEMENT CHARACTER character! Click the "Copy" button below which copies the character into your clipboard, then paste into TikTok's nickname field in your profile. Done!