There were and are a myriad of cultural differences between the North and South of the USA. And between New England, the Midwest and the Pacific North West - all part of "the North". And between, California, the South East, Texas, the "deep" South and the South East - all part of the "South". And, of course, Alaska and Hawaii are each different in their own ways from the alleged monoculture of the continental United States.
However, if the question is about how and why these different cultures chose to become and remain part of the United States then the genesis lies in the fact that the 13 colonies that became the original states were all British colonies and they had that common bond between them. In addition, there was a fair dose of pragmatism: at the signing of the Declaration of Independence, when the colonies were already in rebellion, Benjamin Franklin reportedly said "We must all hang together, or assuredly we shall all hang separately."
Alternatively, if the question is about when the citizens of the United States began to think of the country more as an individual entity (which it is) rather than a federation of sovereign states (which it also is), some research has been done on the use of the phrase "the United States is" versus "the United States are" in decisions of the Supreme Court (admittedly the sample size is small). The latter phrase was overwhelmingly the most common at the beginning of the 19th century, dropping to about 50/50 by the start of the Civil War in 1861. Following the war, which was triggered by disputation between state and federal rights, the use of "are" increased to about 70% in the 1870s, 1880s and 1890s before vanishing completely by the 20th century. Taking this as a guide, the United States really was united around 1900.