chaikathecardocumentary

Tooru/Akari/Shin Acura - Acura, Luxury Vehicle Division of American Honda.
Chaika Trabant/Gaz - The Chaika, a Communist Transporation Wagon produced by GAZ, and the Trabant, produced by East German company VEB Sachsenring.
Guy - Guy Motors, a British company that made cars, trucks, buses, trolleybuses, and armoured cars.
Nikolai Avtotor - Avtotor Factory, a vehicle production factory in Kalinigrad, Russia.
Matthaus Callaway - Callaway Cars, American engine tuning company, works on Chevrolets (Corvettes, etc).
Alberic Gillette - Not sure if he's actually named for automobiles. The closest match is Gillet, a Belgian manufacturer.
Leonardo Stora/Stola - A large stretch, but he may be named after Stora Skedvi, a Swedish town which is home to the production grounds of the Dala7 kit car. If his correct Romanization for his last name is actually "Stola", then he will be named for Stola, an Italian Coachbuilding company that mainly produces concept cars.
Dominica Skoda - Obvious. Skoda Auto, everyone's favourite Czech car maker.
Robert(o?) Abarth - Abarth, Italian automakers who also sell licensed copies of Fiat cars.
Konrad Steinmetz - Steinmetz Opel Tuning, Germans who specialize in tuning Opel cars.
Karen Bombardier - There are so many vehicle related things named Bombardier that it's safer to just assume she's named for all of them. Seriously.
Chaika Bohdan - Bohdan Corporation, a Ukranian manufacturer, and their signature series of buses, also named Bohdan. (You can also spell Bohdan as "Bogdan", but as the Crunchyroll subs use Bohdan, we'll roll with that. Both are correct.)
Selma Kenworth - Kenworth, American truck-makers.
Simon Scania - Scania AB, Swedish manufacturer of commercial vehicles.
Grad Lancia - Lancia, an Italian manufacturer.
Hasumin/Jasmine Orlo - The Orlo Touring Car, a 1904 automobile.

Characters with unknown/no link to cars: Vivi Holopainen, Zita Brusasco, David, Layla, Fredrica, Julia, Frol, Mart, Lavr, Hasumin. From what I've read, Brusasco is an Italian Municipality near Turin, Holopainen is a Finnish surname, and Layla, Fredrica, David, Julia and Mart are just names. Frol and Lavr are probably entirely made up.

Also, places:

Acura Village - Namesake of Tooru, Shin and Akari, and also named for American Honda's Acura division.
Gaz Empire (see also: Neo Gaz Empire) - Namesake of Arthur and Chaika Gaz, and named for GAZ.
Koenigsegg Empire - Named for Swedish manufacturer Koenigsegg, best known for making fast cars and being called "Koenigseggseggsegg" by Jeremy Clarkson.
(The Town of) Iveco - Named for Iveco, an Italian industrial vehicle manufacturer.