Register a brand in e-commerce

Hello everybody
i have a small e-shop and so have website for example www.myredshop.com
and the name of my eshop is red shop .
can i register my e-shop brand in any legal organization ? that prevent other to have a e-shop with my name red shop ?
unfortunately i have a problem due to a new e-shop use exactly my e-shop name with another domain for example www.myredshop1.com !
what can i do ?

I think what you’re looking to do is file a Trademark for your business name.

Trademark - Wikipedia, the free encyclopedia

yes but the matter is that i did not observe any category or class for e-commerce in it , you can register a name for a new software but for an e-shop you cant ( i think ) !
is there any other idea ?

Sure you can.

Just look up the filings on Amazon, Buy.com, Drugstore.com or just about any other major etailer. United States Patent and Trademark Office

BTW, are you in the United States?