If you want a new costume for your character in Scarlet Nexus, you can get it by changing your equipped visuals. Visuals are what the game calls costumes/outfits and you change them by going into your inventory and selecting the visuals tab under equipment.
So to find this tab, first open the inventory by pressing either select or esc. After this, you will then need to select equipment and then visual next to equipments.
That said, From this tab, you then will be able to change and equip various cosmetic items. To do this, hit either enter or A, this will then open the visual menu, and you will be able to change outfits and attachments. As a side note, you can also change the outfit of your companions once you get them using this tab as well.
But how and where do you even get these items, to begin with? In short, you can get quite a few visual items from pre-ordering the game.
So if this is you, can get these pre-order visual items from Satori's store under accept. You can also purchase a few items as you progress in the game at Satori's store aka the save game dude - just look under visuals occasionally to see if there are any items to buy. Once these items are accepted or bought, you will then be able to equip them in the visual tab under your inventory.
Check out all of our guides for Scarlet Nexus on PGG.