However, the British broadcasters placed the similar-looking Australian flag beside the 27-year-old's name, causing irate New Zealand viewers to highlight the mix up on social media.
Formula1.com said Hartley has collected a grid penalty and will drop at least 25 places on Sunday (US time) due to power unit changes.
Brendon Hartley waits to hit the track during his Formula One debut.
It represented a commendable effort, not only given Kvyat has been in Formula One since 2014 but also because it is the New Zealander's first time in a single-seat auto for five years.
Hartley thought his state of affairs was complicated enough for his maiden F1 race, but he'll have to contend with the extra challenge.
Brendon Hartley discusses his car's set-up with the Toro Rosso crew.
Hartley was drafted in by Toro Rosso to replace Pierre Gasly, who is racing in the Japanese Super Formula series this weekend, and made his F1 debut during Friday practice in Austin.
Hartley, a Le Mans 24 Hours victor and world endurance champion, is the first New Zealand driver in Formula One for 33 years.
However, a new engine, MGU-H, hybrid battery and control electronics were fitted to his auto ahead of the opening session, meaning he will take a 25-place drop on Sunday's grid.
The new components incur penalties for exceeding the season's allocation. He also won in Malaysia earlier this month, a day after his birthday.