This name is associated with giving birth to. At this birth, Eve exclaims that she has given birth to a (real) man. Apparently, she saw in Cain at birth that he would become a real masculine man. She saw a lot in him as a person, as a man. Since the name Cain is associated with the word to give life to, Eve may have given this son his name, as she did the third son (Genesis 4:25), although this did not exclude Adam's involvement (Genesis 5:3).

Incidentally, Cain does not have to be the eldest son. The Bible sometimes sheds light on certain events while not mentioning others. For instance, the choice of the author could have been not to mention the birth of earlier/other children than Cain, Abel, and Seth. Later it turns out that Adam and Eve had more children (Genesis 5:4; see also Genesis 4:14).