I am not a lawyer. I am not your lawyer. The following is not legal advice.
Short answer: No, strictly speaking, there are no patent concerns. However, there may be other considerations, namely trademark.
Longer answer: There are three main types of intellectual property (in the US, probably similar in Denmark/EU as well) that would concern you:
Patents: These are "any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof". Not a concern for you.
Copyright: This regards the actual text and content of produced works. So long as you aren't stealing articles and pictures, this doesn't concern you.
Trademark: This is the one that would concern you. Trademark protects against someone masquerading product B for product A. You'd get in trouble if you use the similarity to confuse "a reasonable person" that you're paper, "The Danish Times" is the Times of London, New York Times, the Los Angeles Times, etc. You have two main defenses available here. The first is parody (which I wouldn't use here). The second is that since there are so many papers with a similar naming scheme, a reasonable person would not be confused between the two, or draw any incorrect assumptions between the two.
In answer to your question, you can search the Danish Patent and Trademark Office here, to see if someone already has that trademark: http://searchservices.dkpto.org/trademark--design-searches.aspx. To determine if your trademark would violate a British paper's, consult a lawyer (see disclaimer), preferably one with experience in UK and/or EU trademark law, but I think you are okay.
Source: Memory of a university lecture on IP I attended a few years ago.
EDIT: Upon reflection, if you're basing your name off of British newspapers, you'd be sued by them, in either UK or EU court, so those are the laws in which you need to know about (and probably need your lawyer to know about).