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When you're running a business, your banking needs are likely to be different from your previous personal needs. While you can make do by running your eBay payments through your personal savings and checking accounts, it's much cleaner to establish a separate banking identity for your business.
The best business practice is to set up a merchant or business checking account separate from your personal accounts. While you're not required to do this, if nothing else it will make your record keeping easier. Having a bank account in your business name should also minimize any potential confusion when it comes to depositing or cashing checks made out to your business name or dba.