No, they would be using your trademark if you trademarked your domain name.
This is the way DNS works. It's a list of lists, each list separated by a period.
The first list here is "com"
The second here is "jetsue.com"
The third is "mydomain.jetsue.com"
And "www.mydomain.jetsue.com" is probably just a link to the third list.
The people managing the second list get to decide what is on the third list. What are the lists made of? A text identifer (hostname) an an IP address.
My domain is openvein.org - I can make www.google.openvein.org if I wanted to - doesn't necessarily mean I am linking to Google, copying Google's files, or otherwise doing something without authorization other their using their trademark. All I would be doing is adding a list entry that says a computer listening to a certain IP address can also be known by the name "www.google.openvein.org"
So possibly your domain name is not very original. For example, with millions of people on the Internet, there are bound to be other people using "Atropos" from Greek mythology. And they just might also want a website with that word in the domain, like I did with atropos.openvein.org
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