The name of the country is The United States of America.
We are comprised of states because that's how our system was set up, and, of course, we started off with thirteen colonies, each with their own separate histories, reasons and rationales for having been colonized in the first place and distinctive, unique "personalities". Despite many years of a dominant overall American culture, each state continues to evolve customs and traits which separate themselves from each other.
This is illustrated nicely by comparing Vermont and New Hampshire, for instance: in just about any measure, they are as much a mirror-opposite of each other as they appear to be on a map. New Hampshire is old-school, sectarian Libertarian (Family Values type issues get a very poor play there: they have same-sex marriage on the books) and is taxophobic in the extreme; Vermont is as close to a European-type Socialist state as you'll find in the US (much more than Massachusetts): in fact, they're going to be implementing a single-payer form of health care reform much more like Canada's than the Romneycare found in Massachusetts.
Though there have been separations/secessions within states (Maine was part of Massachusetts once, and West Virginia separated from Virginia during the Civil war), there have never been instances where two or more states have formally dissolved and formed one larger state. Personally, I believe that southeast Florida (Palm Beach county down to and including The Keys) should secede from the Bible-thumping, socially conservative rest of the state. We do not have enough influence in Tallahassee IMO, especialyy compared to the revenue we send them.
Our experiment in federalism is over 200 years old, and has proven to be a fertile laboratory for tinkering with successful and failed political ideas. This freedom is diametrically opposed to the top-down governance of a place like France, where centralized power didn't change one iota after their revolution in the 18th Century.
My own (admittedly rather personal) take on federalism in the US is that diversity is celebrated as one of the core virtues of what makes us unique and special (though I refrain from declaring superiority) and is written into our very DNA as a country. In fact, if anything, I'd prefer to see more power given to the states' rights over self-determination, especially as regards drug policy, for instance, rather than less. If you don't like where you live, you can always move to a different state where more people think as you do and help to create/develop communities where laws focus on your priorities. We've always been a highly mobile nation: I, myself, have lived in seven states and by no means am I unique.