Mobil was the Standard Oil Company of NY after the 1911 Standard Oil breakup by the government.
Its brand was Socony (Standard Oil Co. of NY). The merged with Vacuum Oil to make Socony-Vacuum. Hence, the Vac in Delvac. Mobil became the primary brand, particualy since Socony could only be used in the Northeast. Each Standard oil company could only a Standard derived name in their 'home' region.
The Standard Oil Company of NJ, used the name Esso in the East and outside of the US. It later was renamed Exxon.
The two companies merged and made ExxonMobil, the two biggest parts of Standard Oil reunited.
Interestingly enough, they had a joint venture in some countries prior to remerging called Stanvac (Standard Oil NJ Esso-Socony Vacuum Mobil).