They're called *myname**something* without giving too much away, and the first result that comes up. *myname* seems to be also their stock ticker name. I suspect they might just change their name to *myname* if they had the domain.
A company name, or a stock ticker symbol, is not a trademark unless it is used as a trademark.
It's not clear what you mean by "companies using *myname* in various forms without a trademark". They are either using the term as a trademark - i.e. a brand of goods or services - or they aren't. Again, there is no particular "magic" about whether their mark is registered or not. I might or might not have a license for my dog, but whether or not I own a dog does not depend on whether I've registered my dog with the appropriate government agency. If it has four legs, fur, a tail and says "woof" - it's a dog.
But, let's go back to my first sentence. The stock ticker symbol is assigned by the exchange as an identifier of that company's stock. For example, Verisign markets domain registry services under the mark "VERISIGN". They don't use "VRSN", their stock ticker symbol, as a mark for any goods or services.
Company names, or trade names, are identifiers of the company in question. Whether or not a company name functions as a trademark depends on whether the company uses its name as a trademark for its goods or services. For example, I might run "Bigco Inc." and Bigco Inc. sells a popular line of widgets called the "WonderWidget". Consumers recognize these widgets in the market as the "WonderWidget", and not as "the widgets that Bigco Inc. makes". In that situation, "Bigco Inc." is merely a company name or trade name, but it is not a trademark.
Here's an example of that distinction in action:
http://www.adrforum.com/domaindecisions/1684372.htm
In the montezuma.com dispute, there was a company called "Montezuma Welding and Manufacturing Inc." which was incorporated in 1988. For many years, they sold a line of toolboxes which were branded "CPL" toolboxes (the "CPL" was an acronym they came up with for a unique locking mechanism). They did not call them "Montezuma" toolboxes until much later, after the domain name was registered by the Respondent.
After they changed their branding to "Montezuma" on the toolboxes, they came after the domain name, claiming they had been "Montezuma", as a company, for many years.
But that's not the point. The point was when did they start using "Montezuma" as a trademark.
Now, quite frequently, companies use their trade name as a trademark. Apple Computer makes Apple computers.
So, getting back to my point about Google... if you want to find out whether someone is "using the term" in some manner, then Google is a much better way of finding that out than by looking in trademark databases. In fact, trademark registrations can long outlast actual abandonment of a mark. In the US, trademark registrations are renewed at 6 years, and then 10 year intervals. So, you can easily come across a 25 year old US trademark registration which, in actual reality, was abandoned eight years ago through non-use.
But once you have found some kind of "use", then the next question is whether that "use" is as a trademark, a trade name, or something else entirely. It requires engagement of your brain and learning a bit more about what trademarks are and how they work. If this stuff all depended on some kind of mechanical rule - "is it in some database or not" - then what do you think trademark lawyers do all day?