This cant be done if you are playing the main story for the first time and enter the Chaos level from Chaos Keys as you need to be able to leave the area with your Chaos. What will happen is that the game will save your data and move on to the next level.
What you want to do is select "Stage Select". Chaos level should be one of the available options as long as you've been there once. Grab your little guy and carry him out back to the spawn area. Directly across is the Kindergarten. Go inside and see the Fortune teller. She will come up with a name for your Chaos and you can choose to keep it or have her make a new name. Just take the name she gives you for the Achievement.