Apparently, you can give your Partner Pikachu/Eevee different hairstyles by petting it certain ways, but I don't know which ways will give it said hairstyles.
You have to use two fingers to get the following hairstyles
If you pet their head up and down you get these hairstyles:
If you pet their head in a swirling motion you get these hairstyles:
If you pet their head in a counter-clockwise motion you get these hairstyles:
If you pet their head left and right you get these hairstyles:
You have to use five fingers to get the following hairstyles
Swipe up and down to get these hairstyles:
Swipe diagonally towards the right or swirl their hair to get these hairstyles:
Swirl their hair to get these hairstyles:
The last hairstyle needs ten fingers
Swirl your left hand clockwise and your right hand counter-clockwise to get these hairstyles:
To get rid of their hair swipe left and right continuously
Source
