In order to change Raz's outfit one must finish the optional Scavenger Hunt Side-Quest.
This mission is given early on in the game by Norma and is pretty much impossible to miss.
There are other 'Steam Guides' to help you locate all scavenger hunt items
In order to get every single scavenger item, one must get to the end of the game.

Now! Hopefully you have completed the game and the scavenger item side-quest.
Make sure to turn the side-quest in with Norma. She will be standing next to Lizzie by 'The Classroom'.



After that, a cut-scene shall play and you will be given your original clothes.
Now make your way back to the atrium and head into the 'Noodle Bowl'



Directly to your 'right' from entering the 'Noodle Bowl' there will be a Restroom, activate this door to prompt Raz to change his clothing.



Congrats! Now you can change into the multiple outfits Raz has acquired through his journey, as well as his original clothing.

Hope to have helped you!

If you are feeling generous, or you feel as if this guide helped you, please consider awarding this guide as well as my profile with an award!
Can we get some 'Mind Blown' and or 'Deep Thoughts' Awards for the theme of Psychonauts 2? Also a thumbs up rating is just as helpful if you don't have steam points to spend!
Good luck out there and have fun!