The announcement was made as Toro Rosso racer Kvyat attended the Sochi Autodrom exhibition at the Moscow International Automobile Salon.
"I was amazed to learn there will be a grandstand bearing my name at the Sochi Autodrom - usually, this is an honour reserved for drivers who have retired, so it is both surprising and a great privilege," said the 20-year-old rookie.
The Turn 4 grandstand in question is situated on the inside of the 5.853-kilometre circuit, and offers views of the first section of the track, running from the Turn 2 right-hander through Turns 3, 4 and 5.
"I hope that the spectators will enjoy the fantastic view and have a wonderful time over the weekend of the first ever Russian Grand Prix,” added Kvyat. “It will be a historic time for Formula One and for Russia and I can't wait to race in front of my home crowd."
Kvyat became only the second Russian to compete in Formula One racing earlier this year when he made his debut in Australia, scoring his first points with ninth place. He has since claimed top-10 results in Malaysia, China, Great Britain and Belgium, and is currently 15th in the drivers' championship.
Toro Rosso have already confirmed he will retain his drive in 2015, when he will be partnered by Dutch newcomer Max Verstappen.
The 2014 Formula 1 Russian Grand Prix takes place on October 10-12.