Business name registration is not compulsory to get reseller permit:

It is not required to incorporate the business name to get a sales and use tax permit unless a business name is used to advertise a business. A business name is registered with the county or state under a legal entity structure such as a corporation, limited liability company and an assumed name.

Whether a business is initiated under personal name or business, the owner is personally liable to collect and pay sales tax to the department of revenue. Department of revenue encompasses sales tax liability to all business owners as per their own in the business.

In most states a US citizen or resident mentions a social security number to obtain sales tax permit whereas, a non US resident submits the identification to verify the information.

A business owner is obligated to maintain sales and use tax items list to charge sales tax whether selling online and from storefront.

How does a vendor handle drop shipping order of taxable items?

Generally, a vendor transfers, sales tax liability on the drop shipper's shoulder of the state. Below is described a citation to understand a cycle of drop shipping orders of taxable goods.

Citation of a sales tax order:

A New York state vendor receives an order from a New Jersey buyer of a taxable item.  New York vendor forwards the order to a New Jersey Vendor to ship it to New Jersey buyer and collect sales tax.

Whom to pay sales tax?

In the above mentioned example; Sales tax is payable to the New Jersey Division of Taxation and Finance which is collected from a New Jersey buyer. Though the original order was received from a New York vendor.

A New York vendor generally gets an affiliation fee to push a customer to a vendor who is located in New Jersey in this specific transaction.

A drop shipper is generally a supplier of the state where a buyer is located.