Why does Alex call Laurens "Jack"

His middle name is jack and that's why Hamilton calls him jack or jackie

Jacks a nickname for John, it later became a seperate name

If I don't wrong, Jack is a family nickname for John

Historically, John Laurens’ close friends and family would call him “Jack” or “Jackie.” In Hamilton’s case, he is one of Laurens’ close friends, therefore, he could call him “Jack” or “Jackie” if he wanted to! ^^

It's like how people called Henry's Harry's back then. Though they are their own name now Jack was supposedly a shorter version of John. Jack was also a shorter version of the name Jacob and sometimes James.