If you upgrade your personal PayPal account to a Business account (or open a separate PayPal Business account), you can specify a Business Name in your PayPal account settings that would appear during checkout and in PayPal's records of payments you receive. This upgrade wouldn't cost anything extra and is a good idea anyway, as it would lift the monthly payment receiving limit for personal accounts, among other business-minded amenities.
You can also upload a custom logo/header image by going to Seller Admin > Edit Profile > Upload Your Logo. This image would be shown instead of your Business Name in the header of your PayPal checkouts.