What does “Call things by their name” mean?

Short and simple, being blunt and speak the truth . Yes it is similar to "Call spade a spade".

Here is Confucius's own exposition, provided via Peter Hitchens:

If names be not correct, language is not in accordance with the truth of things. If language be not in accordance with the truth of things, affairs cannot be conducted successfully. When affairs cannot be conducted successfully, propriety will not flourish. When propriety does not flourish, punishments will not be properly meted out. When punishments are not properly meted out, the people will not know how to conduct themselves.’

In the context of relations between Germany and other nations, Merkel is suggesting that frankness and clear speech about contentious issues actually opens a way forward to trust and respect, when compared to an approach of avoiding embarassing subjects for the sake of harmony.

As I searched the quote "The beginning of wisdom is to call things by their proper name." I found its original Chinese is 名正才能言順, which corresponds to the four-character chengyu 名正言順 míng zhèng yán shùn in modern Mandarin. It literally means legitimate name, smooth wording, so it figuratively and actually means "legitimate" or "perfectly justifiable". It's often used to indicate the authenticity of a quality or title someone holds, say, a 名正言順 wife indicates she is the genuine wife of the husband married through a series of customary and legal procedures, a 名正言順 PhD is a title gained through genuine ways, and so on. Although this is in the Chinese context, I think it's also applies in this context.

It means to refer to things using the most accurate word, even if it's hurtful, awkward, or uncomfortable, instead of using euphemisms or dancing around the subject.

http://www.english-test.net/forum/ftopic55704.html

In regards to the Confucius quote, I think that has more to do with his philosophy, rather than the English phrase. But I'm not an expert.

For the sake of completeness, I feel I should point out that this is not an English phrase as such but rather the literal translation of a German idiom. The German phrase is "die Dinge beim Namen nennen". Some functional translations would be: "to discuss a difficult topic directly" or "to address uncomfortable topics head-on".