Coming directly from the Hebrew word אדם (ʾadam), meaning "man" or "humankind," the name Adam was the name of the first man created in Genesis. Interestingly, in Genesis 1:26, the word אדם (ʾadam) is clearly plural and means "humankind," as the accompanying verbs are plural and two people are created as a result. (For instance, Genesis 1:26 says, "Let them have dominion," while verse 27 reads, "in the image of God he created them.") However, in Genesis 2:7, the text says that God formed the man (האדם) "from the dust of the ground," while Genesis 2:15 says "the LORD God took the man (האדם) and put him in the garden of Eden to till it and keep it."
Interestingly, different English versions of the Bible throughout history have separately determined when to begin calling "the man" Adam in their translations. Many don't begin calling the man (האדם) Adam until Genesis 4:25, because it is the first time following Genesis 1:26 (when God decided to create "humankind") that the definite article—the Hebrew letter heh—is not prefixed to the word. So essentially, up until Genesis 4:25, האדם means "the man," while beginning with Genesis 4:25, we begin to read אדם, or Adam. But he will always be "the man."