The United States is the only country that has Exxon gas stations. They're called Esso everywhere else.
In fact, in many states, Exxon is banned from using the Esso name.
Why? The dominant oil company, Standard Oil, was broken up by the Supreme Court in 1911. It was divided into smaller regional companies, (e.g. Standard Oil of New Jersey, Standard Oil Company of New York, etc.) These smaller companies were allowed to use the name "Standard" but only in the states in their own region.
Standard Oil of New Jersey started going by "Esso" (Standard Oil->S.O.->Esso). They had the rights to use the name Esso in New Jersey, Maryland, West Virginia, Virginia, North Carolina, South Carolina, and the District of Columbia. They later acquired the rights in Pennsylvania, Delaware, Arkansas, Tennessee, and Louisiana. However, the other Standard Oil companies objected to the use of the "Esso" name in the other states.
Standard Oil of New Jersey renamed themselves to "Exxon" in 1973, and they named all their U.S. gas stations Exxon to avoid all the complications. They still use the name "Esso" in other countries.