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A vote had been under way across the country to rename airports in dozens of cities. The results were announced on national television.
Pushkin's name will be added to the name of the Soviet-era airport, Sheremetyevo said in a statement.
Authorities are expected to sign off on proposed changes at a later date.
"We will support this decision," Sheremetyevo spokeswoman Anna Zakharenkova told AFP.
Domodedovo Airport, Moscow's showcase transport hub, will bear the name of 18th century scientist and polymath Mikhail Lomonosov.
Yuzhno-Sakhalinsk Airport on Sakhalin Island north of Japan will be named after celebrated playwright and author Anton Chekhov.
Murmansk Airport in northwest Russia will bear the name of Tsar Nicolas II who was executed with his family by the Bolsheviks in 1918.