It would be nice to believe that people would look at the discussions linked above.
But, let me re-phrase the question.
"What is the best way to find out if someone is using (insert characters) which functions in the relevant market for their goods or services as a distinctive identifier of the goods or services they sell?"
Try answering that question instead. What would you do, in order to find out whether someone is using (whatever) as a distinctive identifier on goods or services offered for sale?
Because - and I want to be clear about this - a number of people are going to provide links to trademark registration databases.
The problem with that is both of these scenarios:
1. It is possible for there to be a trademark, and no trademark registration in any database.
2. It is possible for there to be a trademark registration in some database, and no trademark.
And, to save time explaining this again, if those sentences trouble you, then consider the following two questions:
A. Is it possible to own a dog, but not to have a valid dog license?
B. Is it possible to have a valid dog license, but not to own a dog?
The answer to both of those questions is "yes". The same is true of trademarks.