Mark Twain was a master at the art of satire. The significance behind the animal names, fifteen minute nag, Andrew Jackson, and Dan'l Webster is to convey distinct personalities to the reader. Twain uses satire to deliver his commentary on a particular subject. The sarcasm behind the fifteen minute nag is perhaps a comment on the relationships between men and women. Women might start off slow with their intent, however after fifteen minutes of "nagging" they usually "win". General and President Andrew Jackson's personality was at the very least "noticable". This corresponds to his character in the story in that he has a tough and rumble way about him. Dan'l Webster demonstrates the sure bet. He is so smart people are willing to pay attention to every move he makes, similar to how Americans paid attention to the real Daniel Webster. Twain had an uncanny ability to force the reader to either self-evaluate or re-evaluate their own personal character. Using animals to exaggerate the obvious is the very definition of wit.
The animals are named after various important figures in American history. Andrew Jackson, the dog, was named after the seventh president. Daniel Webster is the frog—and was the name of a major lawyer and orator (public speaker) who was Secretary of State. Using these names marks the story as American. It indicates when the story was set (pre-Civil War). It introduces a quiet but ongoing note of humor, because people can imagine the famous lawyer jumping for flies. Finally, it can function as political satire.
Three of the animals in this story are named:
The Fifteen Minute Nag, Andrew Jackson, and Dan'l Webster;
The horse gets her name from being so slow in races--at least at first--but somehow, she always wins. Of course, she doesn't really take a full 15 minutes to run, but her slow starts earn her the nickname anyway.
Andrew Jackson is Jim Smiley's fighting dog. He is probably named for the former president and famous general because they are both extremely tough and unstoppable in a battle. The real Jackson earned the nicknam "Old Hickory" becaue he was so tough. It is only a fluke situation that results in Andrew Jackson (the dog) losing his last dogfight.
Dan'l Webster is the jumping frog that Smiley bets on. He is named after Daniel Webster, a great American statesman and orator. Smiley says that his frog is very educatated (at least as much as frogs can be). So he may have named him because both the frog and the man were exceptionally brilliant.
For mor information about characters and biographies on the real Andrew Jackson and Daniel Webster, see the links below: