Resident Evil 2 comes with a range of different costumes, and it's easy to change them any time you feel like it. Some costumes are unlocked by playing the game, such as getting the Alternative Costume by completing the main scenario. Other costumes are tied to DLCs, pre-orders etc., and are only available if you get them this way.
Anyway, if you have a costume to equip, click on Options (Esc or the keyboard) and select "Costumes" from the menu. This gives you a list of all the costumes you have unlocked, and simply just choose from any of these. Both Claire and Leon can equip costumes.
If you want to go back to normal, choose the "Normal" costume to play without any costumes at all.
You can change your costume at any point in the game, as long as you can access the menu. So don't feel obliged to wear a certain costume, and just change when you feel like it.