Hi Nicole and welcome to the forum
Since you have your tax id, it won't be difficult to find a supplier to work with. You will be able to choose dropship or wholesale with that id. You can indeed go straight to eBay and list your items there for sale if you want, you can choose any selling platform you would like, just make sure you are aware of any fees that are involved, both up front and on sale fees that will impact your margin.
You don't need a company name to trade on eBay, just an eBay id. Of course you can register a business name if you wanted to, it is a good marketing tool to use.
You don't need your own website, but I think it's something you should definitely consider to develop as a long term selling strategy.
I would suggest reading this, it might give you some ideas regarding a marketing strategy.Link hidden: Login to view