No, you don't have to have a business checking account, unless a corporation. It depends on the business type, if a simple sole proprietor, the business name doesn't have to match, just the register owner's name does (as you are Doing Business As). You can also change your ebay name to match a checking account to enroll in Managed Payments, then once enrolled, change your ebay name to something else.
You also might want to use a business account, if you have a tax certificate in that name to purchase items tax free for resale. Otherwise, ebay doesn't care whether business name or not. I might note that sometimes business accounts on some sites come with additional benefits. For instance on PayPal it gives you expanded accounting information. On Amazon it gives you extra discounts and bulk buying perks.
