"Then how can I make sure the acronym/2 letter domain that I bought is not trademarked anywhere in the world??"
The more appropriate question is *why* would you want to make sure of that?
In another thread here, someone is looking for a "consistent" rule on acronymic domain names. There can't be a one-size-fits-all rule, because not all trademarks are created equal, and the assumptions one might make about a registrant in one place are not the same assumptions you would make about a registrant elsewhere.
http://arbiter.wipo.int/domains/decisions/html/2000/d2000-0527.html
-----------------------------------
The Panel considers, on balance, that the Complainant has not proved the registration of the domain name in bad faith. The name was registered as one of a list of generic names, some being combinations of 2 letters or 3 letters. The Complainantââ¬â¢s mark is not one known worldwide as, for example, the letters "BP". From the evidence, the mark "VZ" is well known only in Switzerland and to some extent in Germany and has been registered only in Switzerland. There are two inferences to be drawn from the domain name registration. Either:
the Respondent, as a "wholesaler" of catchy names for domain sites, registered "vz", along with other 2 or 3 letter combinations in the hope of being able to sell the combination of letters to someone wanting a catchy logo or easily-remembered mode of recognition by the public; or
the Respondent was or should have been aware of the Complainantââ¬â¢s logo and registered the domain name "vz.com" with the aim of negotiating a sale to the Complainant at a later date.
There is no evidence to support the latter inference. Accordingly, the Panel must fall back on the onus of proof which remains throughout on the Complainant.
------------------
Now, here's the point to consider. IF the Respondent had been Swiss, and therefore might have had reason to know that VZ is a well-known trademark there, then the result of this case might have been different.