When the Book of Genesis (4:26) says that “men began to call upon the name of the Lord,” what does it mean?

The meaning of this passage depends on the grammatical structure of the Hebrew text, which is not always precisely reflected in English translation. The most probable sense of the phrase is that in this period people first called the Lord "Jehovah." There are a few possible ways to read this.

One way has to do with the history of Judaism and the way the Bible tries to integrate historical and sacred history. Before the Mosaic books were first composed as a part of oral tradition, there was probably some diffuse form of monotheism that gradually evolved in the Levant. This may have been an outgrowth of polytheism, with one god emerging as the most powerful among many. This passage could reflect that historical evolution in some way, describing how a monotheistic worship of a god called "Jehovah" evolved.

A more theological reading might emphasize that the giving of a name, Jehovah, to God, reflected the ways humans and human language had degenerated from an earlier prelapsarian state of immediate apprehension of God to one where God became mediated through books and language.