I think PayPal has different accounts for business or personal. I know I already had a personal PayPal account but when I setup my store I created a new one for my business. When I log into PayPal and click "Profile" there is a section for Business Information where I have my business name. Maybe they don't have that for personal accounts.
I don't "think" we are passing the business name to PayPal, though I'm not 100% sure without checking the code, but if we are passing it we would be getting it from Store Settings under the WebStore administration menu, so you can try putting your business name there (I have my business name there), but if that doesn't work look into getting a business account at PayPal.
Hope that helps,
Joe