The 'category page image' you upload appears on your designer category page (your shopping page for customers). If you have something for sale on Minted.com, then you have a customer-facing designer category page, like this one. This is a secondary form of profile that presents you to the customer and allows you to further brand and develop your presence on Minted. It's highly personalizable, so make it your own!
Please upload a photo, not a logo, as customers respond much better to individuals. Many of them come to Minted in large part because they want to support independent designers. They want to know who you are!
Your 'hand-written designer name' also appears on your designer category page and is another very personal way to allow customers to make a connection with you and your work.