Despite searching hundreds automobile brands, I can find no brand carrying the name of the town in which it was manufactured, and which town was created because of the manufacture of the car. The only U.S. town that I can find that was specifically created for the manufacture of transportation vehicles was Pullman, Illinois (now part of Chicago), which was created by George Pullman, head of the Pullman Palace Car Co. (later the Pullman Co.). The Pullman Palace Car Co. made railroad passenger cars, and, as far as I can determine, never tried to produce automobiles, although they did produce some automobile bodies for Packard, Moon, and other automobile manufacturers.
There was, however, a Pullman automobile, but it was produced by The Pullman Motor Car Company (1905-1917) of York, Pennsylvania. This company was founded by A. P. Broomell, and was in no way related to the Pullman Company, except that the choice of the automobile name was apparently intended to reflect the luxury, and very high quality, of the Pullman railroad cars. Since I have found a few Pullman automobile advertising pictures from about the correct time period, and which resemble the mystery car, I'll take another stab and suggest that the mystery car might be a: 1915/17 Pullman Junior 4 cylinder/5 passenger tourer by The Pullman Motor Car Company of York, PA.