If it is not capitalized or italicized the name refers to any rod-shaped bacterium.[2]
There is no connection between the shape of a bacterium and its colors in the gram staining. In other words, some of them are gram negative and some are gram positive.
↑S. Srivastava; Prem S. Srivastava, Understanding Bacteria (Dordrecht; Boston; London: Kluwer Academic Publishing, 2003), p. 61
↑ 2.02.1Paul G. Engelkirk; et al 2011. Burton's microbiology for the health sciences. Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins, p. 53.