After several changes over the years, the Episcopal Church is now officially named the "Episcopal Church in the United States of America" (ECUSA). Prior to the Revolution the Church was simply the Church of England (CoE), with its official head the reigning British Monarch. This simply wouldn't do for a church in a newly independent republic with a strong distaste for monarchy and a Constitution that forbade both titles of nobility and an established church. If it weren't for the fact that a large number of the Founding Fathers, including three of the first four elected presidents, as well as other influential and wealthy cultural, intellectual, and economic leaders in the new nation shared a strong adherence to the forms of CoE worship and hierarchical "episcopal" structure as well as to Anglican intellectual traditions, its probable that the remnants of the CoE in the US would have been eventually subsumed into Methodism, Presbyterianism, or other relatively moderate Protestant sects sharing an origin in the British Isles. Frankly, its hard to imagine the former CoE surviving in the US without having "episcopal" as important part of its name. More than anything else, it was adherence to the belief that the Church of England (and its American offshoot) had an unbroken pattern of apostolic succession of ordained Bishops gong back to the early Church in Rome that defined it. Perhaps "American Episcopal Church" or "Episcopal Protestant Church of America" may have worked.
Today, a name such as "Anglican Church in the United States" might nicely sum up what the Episcopal church could alternatively be known as today, since that is essentially what it is: the sole branch of the Anglican Communion in the United States formally recognized by the Archbishop of Canterbury.