Pokemon Brilliant Diamond & Shining Pearl brings a few character customization options. Some of these customizations are permanent (Gender, Skin Color), which you can choose during character creation. Outfits and Hairstyle can be changed during the game but you will have to progress further deep in the came.
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To be able to change the Outfit and Hairstyle, progress in the game until you reach Veilstone City. In the southern portion of Veilstone City, you will Metronome Style Shop (the Purple roof building in the second picture below). Go inside the Metronome Style Shop and talk to the girl at the reception to check various available style options. One limitation here is that you cannot individually select your outfit and hairstyle. You can only choose a style that comes with an outfit and a hairstyle. You can purchase the styles using Pokedollars.