Barb, my initial instincts were generally on the right track in regard to source materials--at pp. 93-95, The History and Biography of Linn County Missouri provides a pretty good profile of the formation of Company A, 6th Missouri Volunteer Infantry. It mustered in July 20, 1898, trained at Jefferson Barracks in Missouri, and was stationed at Jacksonville, Fl., Savannah, Ga., and Havana, Cuba, during the Spanish-American War. It did not engage in any combat, however.
Regarding the nickname of the company, the Argus Rifles, The Encylopedia of the History of Missouri, vol. 3, p. 98, (published in 1901) tells us that the publisher of the Brookfield Argus was Charles W. Green, that his politics were Progressive and Democratic, and that his newspaper was a Democrat newspaper.
A general history of the Spanish-American War tells us that war was instigated in large part by the "yellow journalism" of the Democrat press, generally, and more specifically by William Randolph Hearst, who owned the New York Journal, and Joseph Pulitzer, who owned the New York World and the St. Louis Post-Dispatch. Both Pulitzer and Hearst were Democrats and their newspapers were Democrat newspapers.
For the role of the Democrat press in the start of the Spanish-American War, a good place to start is with W.A. Swanberg's book, "Pulitzer."
Anyway, I would bet a little research would reveal that the Brookfield Argus and Charles W. Green were walking in political lock-step with Pulitzer and Hearst, and that Brookfield Argus support for the war had an effect on the men of Brookfield, as well as the naming of the local unit that answered the call to arms.
Of course there might be those who think it mere coincidence that the local military unit bore the very same name as the local politically-oriented newspaper that agitated in favor of the war and was at the forefront of the call to arms.