In 1911, the United States Supreme Court broke up The Standard Oil Company into 34 separate companies as part of an antitrust lawsuit. Each of these 34 companies were allowed to retain the name of Standard Oil, provided that each of these companies only used the name in their designated geographic region.
One of the 34 companies was called Standard Oil (New Jersey), which chose to call itself Esso, because it was the phonetic spelling for the letters "S.O.", which stood for "Standard Oil".
So Esso was the oil and gas company that was allowed to sell its products in the New Jersey area using the emblems, name, and initials of its former parent, Standard Oil. In 1966, Esso decided that it wanted to market its oil and gas products throughout the United States, but in order to do so they would be required by the previous Supreme Court decision to abandon any use of the Standard Oil trademarks, including the use of its initials in the phonetic "Esso". Thus, a new name was chosen: Exxon. In 1972, the shareholders of Esso approved the name change and the signs at all Esso service stations in the United States were changed to Exxon.
Exxon merged with Mobil in 1999 and is now called ExxonMobil. In 2005, ExxonMobil was the most profitable corporation in the world claiming over $36.1 billion in profit on $371 billion in revenues. This was the largest yearly profit for a single corporation in history.
ExxonMobil still uses the name brand of Esso outside of the United States. For example there is an Esso, U.K., and an Esso Australia Pty Ltd. Outside the U.S. there are many other companies named Esso that are almost all owned by parent ExxonMobil. One exception is Esso in Canada, which is owned by another company that just owns the rights to market gasoline in Canada under that name brand.