William "Martin Murphy, the Bantry jobber," was a businessman from County Cork who became hugely influential in the "national press." He was elected to the House of Commons in 1885 and became a member of "the Bantry band," a group of MPs who all came from the vicinity of Bantry Bay. He published the newspaper that the Citizen is mocking, "The Irish Independent, if you please, founded by Parnell to be the workingman's friend."
In 1900 Murphy merged several struggling publications (including the Irish Daily Independent, a paper founded by Charles Stewart Parnell after his fall from power) and launched The Daily Independent and Nation, which soon challenged The Freeman's Journal for the claim of being Ireland's leading nationalist newspaper. The Citizen, reading a succession of very Anglo-sounding names from the births, deaths, and marriages lists in the Independent, implies that it, like the Freeman's Journal, is insufficiently nationalistic and excessively cozy with the Anglo-Irish elite. Joyce sometimes said that the United Irishman, a more vigorously nationalistic paper than either the Freeman's Journal or the Independent, was the only Irish newspaper worth reading. And given the fact that Murphy turned against Parnell in the struggles after the O'Shea divorce trial, it seems possible that the author shared some of the Citizen's dislike for Murphy. But the Citizen's words amount to little more than ethnophobia.
For more on the insufficiently studied topic of Murphy's career in journalism, see "Entrepreneurship, Power, and Public Opinion in Ireland; the Career of William Martin Murphy," by Andy Bielenberg, at http://www.ucc.ie/chronicon/bielfra.htm. Murphy is best known to historians for his steadfast opposition to labor unions, which earned him the nickname "William Murder Murphy" after his opposition to unionizing Dublin's tram business led to the greatest labor clash in Irish history, the Dublin Lockout of 1913. It would have been anachronistic for Joyce to allude to this series of events in a book set in 1904, and he does not do so. But he was almost certainly aware that Murphy, in addition to being a titan of Irish journalism, was the man who organized the Dublin United Tramways Company.