Lt. Jimmy Cross's name symbolizes the burden that he has to carry as the reluctant leader of men during wartime. First, his initials are intentionally J.C. (Jesus Christ). While Cross is hardly a Messianic figure for his men, he feels the weight of trying to keep them safe just as Jesus Christ came to "save" mankind.
Similarly, Lt. Cross has his own "cross" to bear. When O'Brien lists the tangible elements that the soldiers carry in the title story, he also notes Jimmy Cross's carrying the responsibility of his men's lives. This creates a comparison between Jesus of Nazareth's carrying the crossbeam to his execution site and Jimmy Cross struggling under his weighty responsibility--each man struggles for others' sake.