The white cat is a purchasable pet at Eeylops Owl Emporium & Magical Menagerie. It can be bought for 9 Galleons. When bought the white cat becomes your icon.
Description[]
"The White Cats often have bright blue eyes which stand out beautifully from their snowy white fur."
Pottermore Playstation Home[]
On Pottermore PlayStation Home, the White Cat is one of the five cats available for purchase at the Magical Menagerie. It must be purchased with real money and costs £2.39.
When purchased, it will walk alongside the player's avatar in the game.