Adam - Meaning of Name
He Called THEIR Name Adam (Man)
The only reason a human being is entitled to the description adam is due to his intellect and emotional life-force, not because of his body. Were it not for this he would be indistinguishable from the animals as we know already from Tehillim 49:13.
See that man had been created "in the image of G-d," he should have reproduced children which fitted the same description. This is indeed what happened when Adam and Chavah begat Shet. Shet represented a combination of intelligence and wisdom, see that the intelligence is the foundation of everything.
The expression even shetiyah (foundation stone), which our Sages applied to the stone in the Second Temple which replaced the original Holy Ark on that site, was so-called because that site was the foundation of the universe (Yuma 53).
The name Shet which Chavah gave to her third son symbolized that he was to be the founding father of all righteous people in the world (seeing the Torah does not relate anything about that is negative). (Rabbi Bachya)