Speaking of New-York, reminds me of some observations which I met with some time since, in one of the public papers, about the name of our state and city. The writer proposes to substitute for the present names, those of the State of Ontario, and the CITY OF MANHATTAN. I concur in his suggestion most heartily. Though born and brought up in the city of New-York, and though I love every stick and stone about it, yet I do not, nor ever did, relish its name. I like neither its sound nor its significance. As to its _significance_, the very adjective _new_ gives to our great commercial metropolis a second-hand character, as if referring to some older, more dignified, and important place, of which it was a mere copy; though in fact, if I am rightly informed, the whole name commemorates a grant by Charles II. to his brother, the duke of York, made in the spirit of royal munificence, of a tract of country which did not belong to him. As to the _sound_, what can you make of it, either in poetry or prose? New-York! Why, Sir, if it were to share the fate of Troy itself; to suffer a ten years' siege, and be sacked and plundered; no modern Homer would ever be able to elevate the name to epic dignity. Now, Sir, ONTARIO would be a name worthy of the empire state. It bears with it the majesty of that internal sea which washes our northwestern shore. Or, if any objection should be made, from its not being completely embraced within our boundaries, there is the MOHEGAN, one of the Indian names for that glorious river, the Hudson, which would furnish an excellent state appellation. So also New-York might be called Manhatta, as it is named in some of the early records, and Manhattan used as the adjective. Manhattan, however, stands well as a substantive, and "Manhattanese," which I observe Mr. COOPER has adopted in some of his writings, would be a very good appellation for a citizen of the commercial metropolis. A word or two more, Mr. Editor, and I have done. We want a NATIONAL NAME. We want it poetically, and we want it politically. With the poetical necessity of the case I shall not trouble myself. I leave it to our poets to tell how they manage to steer that collocation of words, "The United States of North America," down the swelling tide of song, and to float the whole raft out upon the sea of heroic poesy. I am now speaking of the mere purposes of common life. How is a citizen of this republic to designate himself? As an American? There are two Americas, each subdivided into various empires, rapidly rising in importance. As a citizen of the United States? It is a clumsy, lumbering title, yet still it is not distinctive; for we have now the United States of Central America; and heaven knows how many "United States" may spring up under the Proteus changes of Spanish America.