I have my game just about ready to sell (almost done beta testing and such). I plan to sell it on my own websiste through an ecommerce plugin, so do I need any sort of license to sell my game? Do I need to register my business/company name with anything to be able to use it?

You need a business license with your local or regional government, so you can pay taxes on your income.

Which country are you in? In the UK for example, you can (and must) report income to the tax office by writing to them (see their website). (I'm not aware of requiring licences to sell things in general in the UK, be it e-bay stuff or games, but IANAL, so I'd be curious to know if one knows different.)

I'm the US in Texas. I am confused, because on the website where you get your license it says that for a sole proprietership you must get a license for your company name, and for each county you will do business in. Right now, my company is online only and will just be used as a number which I will sell games/apps and such under. I do not have an actual location for my business. What do I do in this situation?

Your home is your business location. My STRONG recommendation is that you contact your local SBA office and ask advice there, AND that you (at least one time) get a professional accounting/tax person to help you get the initial paperwork sorted out.