Register a brand in e-commerce

Hello everybody
i have a small e-shop and so have website for example
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 !
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,, or just about any other major etailer. United States Patent and Trademark Office

BTW, are you in the United States?