Genesis 5:1-3 (ESV)
This is the book of the generations of Adam. When God created man, he made him in the likeness of God. 2 Male and female he created them, and he blessed them and named them Man when they were created. 3 When Adam had lived 130 years, he fathered a son in his own likeness, after his image, and named him Seth.
The word translated “Man” in v2 is “Adam” in Hebrew. So the Adam in v2 refers to human beings generally, while the Adam in v3 refers to a specific man.
The confusion arises here because the Hebrew word אדם (adam) means “earthling”. It is related to the words for earth ‘Adama’ (אדמה) and red ‘adom’ (אדום). So it can refer to any human being (as in Genesis 1:26-27; 5:2). It was also the personal name for the man created in Genesis 2:7, and is used in this way in Genesis 2:20; 3:17,21; 4:1,25; 5:1,3-5.
When it is preceded by the definite article (ha adam or האדם) it is translated as “the man” but when the definite article is dropped it is usually translated as “Adam”. In some cases, if the word appears to be used generically (as in Genesis 5:2), it is also translated as “man”, “human”, “humankind” or “human beings”.