Another tidbit from George R. Stewart’s Names on the Land: A Historical Account of Place-Naming in the United States (p. 58):
Also two brothers named Newce came there [to Virginia] to make a plantation. Once before, in Ireland, they had founded a town, naming it Newcetown, where it still stands. So now to their second settlement they gave the name New, and since it had an anchorage, they called it Port, and it became New Port Newce. The brothers were unfortunate, and men forgot them soon; but men remembered Captain Newport, who had done much to found Virginia. So they began to think and write Newport’s Newce, perhaps even to confuse the second part with Neuse River. Then in trying to make sense they wrote Newport News, and so it remained. Thus with men and names, as with fishes in the sea, the greater often swallow up the smaller.
According to the Wikipedia article, the etymology is disputed, but with what brio Stewart tells the story!
Addendum. A query by AJP in the comment thread prompted me to check the endnotes done for the 1958 edition, where I find an extended discussion which I reproduce below:
Newport News: My account is chiefly based upon Alexander Brown, First Republic in America (1898), p. 459. Work appearing since 1944 throws doubt upon this explanation. See C.W. Evans, “Newport News: What’s in a Name?” in Newport News’ 325 years, A.C. Brown, ed. (1946), and P.B. Rogers [“Place Names on the Virginia Peninsula,” American Speech, 29 (1954):241-56]. Both these writers end in doubt, and Rogers concludes: “It is now time for all to admit freely that . . . nobody today really knows how the city got its name.” I certainly agree, as far as absolute knowledge is concerned. I cannot see, however, that these later writers have wholly negated Brown, especially since in his statements that the last word is spelled Newce, Newse, and Nuce he seems to be using documents to which they have not had access. Moreover, their argument that the name cannot be connected with Thomas Newce because he arrived in Virginia only a few days before its first recorded appearance seems to me reversible. May not this almost simultaneous appearance actually indicate a connection with the Newces? In fact, if it were known that they were to make a settlement there, the place might have been named for them even before their arrival.