Season 6 has brought a lot of new cosmetics to the game and there are a few skins that have different styles to them. These will be unlockable by progressing in level for the Battle Pass skins and the clown skins that were available in the also have different styles. Pets are a new cosmetic that have been added to Fortnite, and it looks like these will have unlockable styles as well. Here are all the unlockable styles for skins and pets for Season 6 in Fortnite Battle Royale, thanks to @TwoEpicBuddies:
You will also be able to change the hat style as can be seen below:
