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Yes, you can do so, as long as there's not a "likelihood of confusion" with other trademarks that are already out there.
The crux of trademark law is "likelihood of confusion". . That is, confusion that consumers will believe the products or services originated or was authorized from the trademark owner. If there is an action against someone using a mark, the court is going to look at the following factors to see if there is such a likelihood:
1. Strength of the mark
2. Proximity of the goods
3. Similarity of the marks
4. Evidence of actual confusion
5. Marketing channels used
6. Type of goods and the degree of care likely to be exercised by the purchaser
7. Defendant's intent in selecting the mark
8. Likelihood of expansion of the product lines
So, for example, if you're trying to start a comic book company or movie studio, "DC" probably wouldn't be accepted because of the current trademarks that are already dominating those industries. But if you're going into lawn maintenance, etc... and there's no likelihood of confusion with your company and a company already in existence and using a trademark, then using your initials would be okay. For example, I have initials of GM, so I could use "GM Law Firm" or something like that. While there's a very large company that uses "GM" (General Motors), the fact that I'm in an entirely different industry and there'd be no likelihood of confusion means that there would not be an infringement. Note that I couldn't go into car manufacturing (or related industries) and hope to use that (as that could lead to a likelihood of confusion).
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Look for the stars on your screen (★★★★★). Thank you, ***** ***** luck to you!