One did not like PUNCHINELLO because it means a "little Punch," and he--the speaking-trumpeter--liked a great deal; and lo! while he spoke, he changed his trumpet for several horns. Then he was taken with a fit of herpetology in his boots, and sank to advise no more. Another--a fellow with an infinite fancy for buffo minstrelsy--was vociferous that PUNCHINELLO should be called "Tommy Dodd." The discussion upon this lasted for three months; but finally, "Tommy Dodd" was rejected on account of the superfluously aristocratic aroma that exhaled from the name. Four divisions of men with banners then came by, each division respectively composed of members of the waning families of Smith, Brown, Jones, and Robinson, and each division bawled and thundered that the name round which it rallied should be adopted instead of PUNCHINELLO, on pain of death. And thousands of others came with suggestions of a like sort; for which some of them wanted "stamps." And when they had all had their say, PUNCHINELLO was called PUNCHINELLO, and nothing else--a name by which he means to stand or fall. And now to business. PUNCHINELLO is not going to define his position here. He refrains from boring his readers with prolix gammon about his foreign and domestic relations. He will content himself (and readers, he hopes) by briefly mentioning that he has foreign and domestic relations in every part of the habitable globe, and that they each and all furnish him with correspondence of the most reliable and spicy character, regularly and for publication. Among his foreign relations he is happy to reckon M. MEISSONNIER, the celebrated French artist, to whom he is indebted for the original painting from which PUNCHINELLO, as he appears on his own title-page, is taken. A preface is not the place in which to enlarge upon topics of great humanitarian interest, political importance, or social progress. PUNCHINELLO will merely touch a few of such matters, then, and these with a light finger. (No allusion, here, to the "light-fingered gentry," for whom PUNCHINELLO keeps a large grape vine in pickle.) PUNCHINELLO observes the incipient tendency to return to specie payments. To this revival, however, he is not as yet prepared to give his adhesion, though, on the whole, he considers it preferable to relapsing fever, which is also noted on 'Change. Cuba shall have her due share of attention from him. And if She-Cuba, (Queen of the Antilles, you know,) why not also He-Cuba?--lovely and preposterous woman, who, from her eagerness to slip on certain habiliments that are masculine, but shall here be nameless, shall henceforth be appropriately distinguished by that name. Let other important topics take care of themselves. PUNCHINELLO will only add that he would at any time rather suspend the public plunderers than _habeas corpus_, and that he means to take the gloss off the grim joke that "Hanging for murder's played out in New-York."