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That depends on various factors. Individuals are not allowed to have a business, or ecommerce merchant account, so your ecommerce business would have to be a business, not just you acting as a business. You'll most likely have to have a Federal Tax ID number established and a separate business checking account. If your ecommerce site is more of a hobby than a business it may not warrant the extra expense of an ecommerce merchant account.
The bank providing the ecommerce merchant account will look at your business' credit rating and your personal credit rating; if either has black marks the odds are the account won't be approved. Another factor is the volume of sales. If your ecommerce business generates less than $1000 per month in sales then it wouldn't make sense for you to have an ecommerce merchant account. The fees would eat into your profit margin.
You also should consider the number of sales transactions your ecommerce site generates per month and what you sell. There are alternatives to your own ecommerce merchant account and that's using a third party processor. Your site can accept credit cards through the third party. You don't have to have a secure site, gateway, or pay the monthly statement fees.