There's really two questions here. How does propaganda work and what did the German's know about how it worked?
What is Propaganda
Applied rhetorics for the persuasion of mass audiences through the use of mass media for the purposes of commercial interests (eg advertising, public relations) or to persuade audiences to support a cause or to hurt support for the opposing side's cause (war-time, political, advocacy, lobbying)
Different Avenues of Propaganda
There are avenues of propaganda: white, grey and black propaganda. White propaganda is when the source of the propaganda is known and black is when the source is a lie. Grey is when the source unknown. Usually when we think of the word "propaganda" we think of black propaganda, but white sources are very common and also effective. Goebbels is an example of white propaganda. The White House press secretary is another example, although I'm not trying to draw a direct parallel. Advertising is another white source and quite effective. Maybe we don't think of advertising as "propaganda" but we know its advertising, and it still helps companies sell products. Therefore, propaganda absolutely does not need to hide its source to be effective.
Title of Ministry of Propaganda
Germany was ground-breaking in the field of propaganda in the early 20th century. America had a negative attitude towards it even during WWI and limited its use. American intellectuals developed a model based on a poor understanding of human behavior that envisioned propaganda directly entering the audiences thoughts and influencing them directly without any feedback or interpretation by the audience. Therefore the American interpretation of propaganda was as a very dangerous weapon that could destroy democracy.
The German interpretation was not nearly so dire. Propaganda can also be seen as a tool to spread positive political ideas. We use propaganda today this way although we do not call it by that name due to the negative connotation. It might be best to translate Goebbels as the head of the "Ministry of Public Information" or "Ministry for Advocacy for the Interests of German Peoples" to understand how the German people would have understood him.