What is the name of Batman's car?

Before the familiar bat-finned cars, the title "Batmobile" was first used on a red convertible in Detective Comics #48 in February 1941. Most of the design was based on the 1936 Cord, though the nose of the car looked more like that of a Lincoln or similar car. The bat mask did not exist yet, but the car did sport a small "bat" hood ornament.

Several "Proto-Batmobiles" had appeared in comics by this point, though this was was the first to use the name. It was also the last car used before the now famous Batmobiles with the bat-masks and roof fins.

http://www.batmobilehistory.com/1941prebat-batmobile.php

The Batmobile.
http://www.1966batmobile.com/