As others have said you can’t copyright a name. The best example are song titles. “Cherish” by Kool and The Gang, and by Madonna and by The Association. All different songs, and all the same name.
A trademark is a bit different and the Internet has effected this somewhat.
In the old days you could have two people with the same name holding the same trademark. In fact you still can but due to the Internet it’s a bit harder.
For example let’s say I have a business called “Mark’s hardware.” My business is located soley in Chicagoland. Suppose some in Houston decides to open a store called “Mark’s hardware,” and that store is located exclusively in Houston.
Since the territories are so far apart and neither one does business in the other’s territory, both trademarked names would be likely to be valid.
In other words no one in the Houston or Chicago area could use the name “Mark’s hardware,” but in other areas of the country you’d be able to
Now, Walmart, Sears, Target,etc these are stores with national presence. Even if your particular area didn’t have a Target for fifty miles it’d be imossible to have another store with a trademark name was Walmart or Target.
This was once the standard for trademarks. With the Internet this has been erroded. After all you put Mark’s Hardware into a search engine and it’ll come up regardless where it is. There is no “terrority” on the Internet.
You also have an area called use specific trademark names. For instance, Joel Hyatt in Chicago was a lawyer and advertised “Hyatt Legal Service” Hyatt Hotels sued and won, but on appeal and all the way up, Hyatt lost. The appeals courts kept ruling, since Hyatt is HOTELS and this man is Hyatt LEAGAL SERVICES, there is no conflict.
The case was finally resolved with Hyatt Legal Services winning but putting a disclaimer on their ads “not affilaited with Hyatt Hotels”
Domain name squatting is another huge issue in itself. This is basically taking a domain name, possibly tradmarked name and holding it without having any “valid” use for it.
This is why many people “park” their domains. Let’s say I register “Markxxx.Com” and don’t do anything with it. Then let’s say a guy forms a band called “Markxxx” and sues me for trademark infrignment and squatting on his domain name.
Because I have never done anything with that domain name one could argue that I am not entitled to it. If I “park” it or put some info on that domain name, like one of those search sites on it, I could argue my having it serves a purpose.
Would I win in that case? Who knows a judge would decide.