With the breakup of Standard Oil in 1911, each of the surviving companies that marketed petroleum products was assigned a territory in which they were allowed to use the Standard name and certain other trademarks associated with Standard from before the breakup, including Red Crown or Crown Gasoline and Polarine Motor Oils.
Along the eastern seaboard, Standard Oil of New Jersey (Esso/later Exxon) was assigned to market in New Jersey, Delaware, Maryland, Virginia, West Virginia, North Carolina and South Carolina. Two subsidiary companies were part of SONJ, including Standard of Pennsylvania (marketing in Pennsylvania) and Standard of Louisiana (marketing in Tennessee, Arkansas, and Louisiana). Through purchases in the early 1930s SONJ moved into New England, but this dominant marketer was barred from direct operations in Georgia, Florida, Mississippi, Alabama, and Kentucky.
Standard Oil Company of Kentucky(KYSO), one of the surviving Standard siblings, was assigned marketing in those five southern states. Without production or refining capabilities, KYSO acted as a large gasoline "jobber", distributing products manufactured by others, particularly gasoline refined by Esso and lubricants by Mobil. In 1961, however, Standard Oil of California purchased Standard of Kentucky, and as quickly as possible dropped all of the purchasing agreements with Esso and Mobil. Kyso stations were reimaged between 1962 and 1964 and Kyso "Crown" and "Crown Extra" were replaced by Chevron and Chevron Supreme gasolines. Station brand identification retained the "Standard Oil" signage as always, although the colors were reversed from the previous logo.
This arrangement was not unusual for Chevron. On the west coast Standard of California had owned and operated "Standard" stations since 1911, and had sold gasolines branded "Chevron" through these stations since the end of World War II. Standard's dealer network, not the company owned stations, began in the 1920s under originally the "Standard / Authorized Dealer" network and, as they expanded outside of their assigned territory in the 1930s, under the name "Calso". The Chevron name came from the hallmark logo first used in the early 1930s, and was applied only to gasolines at first. The Calso network in the Rocky Mountain West changed to "Chevron Stations" in 1946, as were the Standard dealer sites, company owned stations retained the Standard name; also in 1946 Calso was introduced as a jobber brand in the northeast and stations were eventually found from Maine to eastern Virginia until 1959, when those stations branded Chevron.
The Kyso purchase put Standard of California, through their new subsidiary, Standard of Kentucky, in a growing market in the 1960s. To tie in to existing marketing areas, Standard of Kentucky began operating some stations in Tennessee under the Chevron (not Standard) name, as well as around Bristol, Virginia. They signed on a jobber with some 40 stations in South Carolina in the 1970s (Spartan Petroleum, formerly an Atlantic jobber) that put the Chevron sign in NC for the first time, on I-26 at Naples, NC in 1977. By this time Standard stations in Florida, Georgia, Alabama, Mississippi and Kentucky were displaying the "two stripe" Chevron sign with the word "Standard" across the top, as were genuine company owned stations in Standard of California's native territory out west. Identical signs displaying Chevron were used in the west for dealer stations and in all states where the Standard name was not allowed. By the early 1980s all of the Standard branding was phased out, except for the token stations listed in this thread, and the Chevron name was used otherwise universally.
I was in Virginia when Chevron purchased Gulf in 1984. During the summer of 1985 Gulf stations in Virginia, Maryland, Delaware, West Virginia, Texas, Louisiana, Oklahoma, and some border areas were all converted to Chevron. We photographed a number of thse sites being reimaged at that time. Shortly after that Chevron (former Calso) and Gulf stations in the northeast were sold off piecemeal and to Cumberland Farms, who still operates under the Gulf name up north. Gulf in the south, in the former Kyso area, was sold to BP to prevent anti-trust action.
For more information about the relationships of the Standard siblings, I recommend my book "Standard Oil, The First 125 years". It is out of print, but I do see them on eBay and Amazon and in used book stores.