Yes, it is the Declaration of Indepedence, because it was the document used to break off from England. The document also stated some of the principles of the French Enlightenment, that people have inalienable rights that must be recognized by a government only for the reason that a person is human and exists in the world.
From a strict constructionist view of our founding documents, it is pretty clear that the founders and framers of this country wanted to have a very limited government with checks and balances and they did not intend for our people to be too dependent. Having said that, people must work together and pay taxes to meet the basic needs of government to fulfill the ideals in the Declaration of Independence. Basically, it states that people should expect that the government will protect life, liberty, and the pursuit of happiness.
The document drafted July 4, 1776 is the Declaration of Independence. I don't see how it would be called or be named Interdependence. Its declaring our freedom from a tyrannical power. It allowed us to seek freedom from many different persecution that government was throwing down a the current time.
When the Declaration of Independence was signed on July 4, 1776, the thirteen colonies formally declared their independence from the British Empire, eventually leading to the Revolutionary War and the foundation of the government of the United States of America. John Adams suggested that Thomas Jefferson compose those first draft, and the first signee, John Hancock, has had his name associated with signatures ever since.
The official title for the document is the Declaration of Independence. I really don't see the relation to Interdependence. The Declaration of Independence was written after America was freed from the British Empire, which made the United States its own independent nation. While word-play may seem like fun now, the title was very fitting at the time.