An auto racing group failed to show that “National Midget Series” had acquired meaning to consumers beyond its literal words, the Trademark Trial Appeal Board said in rejecting its application.

The board said June 5 Performance Open Wheel Racing Inc. didn’t demonstrate that consumers identified the proposed mark with a particular source, a requirement to register a merely descriptive trademark. Rival United States Auto Club Inc., which challenged the application, has used the mark since 2004, including at joint events...