You can change most of your appearance from the pause menu. This menu is unlocked during Main Mission 3, right after leaving Mabel’s Research Lab.
Open the menu with X and then press - (minus button) to enter the Outfit menu for clothing customization. From here, you can press ZR to move to the Looks menu where you can change your eyes and other facial features.
To change your hair style, you must visit a salon. There are five salons in total. Four are located in shopping arcades:
Passage du Palais (Next to the Rouge Pokémon Center in the top center of the map)
Passage Ombragé (Rouge Sector 4)
Galerie de la Lune (Rouge Sector 2)
Promenade du Vent (Vernal Avenue - Vert Sector 9)
And the final one, Coiffure Clips, is located on Bleu Street across from the Bleu Pokémon Center
Interactive Map.