At the risk of sounding insensitive, why are they so long? Do they have a meaning in their native language? Is there a reason or some kind of system that determines what they are?
Just wondering and thanks.
Indian names? Did you mean names like Tashunka Witko and Tatanka Yotanka, or names like Sivakumaran Mahalingam?
Well, I’ll take your question to refer to America’s original inhabitants.
AFAIK, every native dialect used names descriptively. Whether it was a name for a person, or a place name, it generally referred to a unique feature or characteristic. Places were usually named based on the original encounter. If you discovered a valley with a lake at the bottom, that lake would likely become known as “Lake At The Bottom Of The Valley”.
The Chippewa from the area of Lake Superior called the lake Kitchi-gummi, which simply meant “Great Water” in Chippewan.
Being from the Long Island, NY area, I grew up seeing Indian names all over, right on out to Montauk Point. Lake Ronkonkoma, or Raconkamuck, was a boundary between the Nissequogue, Setauket, Secatogue and Unkechaug tribes of Long Island. Raconkamuck means “The Boundary Fishing Place”
So the Indian Chief (who by this tribe’s tradition named all of the children) says, “When a child is born and I see a great bison, the child is named Great Bison. When a child is born and I see a running deer, the child is named Running Deer. But tell me: Why do you ask, Two Dogs Humping?”
I think the OP means actual Indian names. Like the Simpsons spoofed with Apu Nahasapeemapetilon. Sorry, I don’t know why they’re so long.
Yeah, I knew that. But since American Aboriginals were brought up, I couldn’t resist the joke. 
BTW: I’m sorry (really, I am) but Prime Minister Vajpayee’s name sounds amusing in English. “Vodge pie”? What’s a “vodge”?
Now, now. I told you I was sorry. I just can’t help myself. 
India has so many cultures, for instance, there was a famous military leader in India with the exotic name of “James Skinner” (half Scotsman, half Rajput, a volitaile combination). But as far as “native” names are concerned, Tamils seem to have the really long surnames, in the 4 or more syllable range. Other than that, many Indian surnames don’t seem too long (e.g. Singh, Patel, Gandhi, Nehru). The first names can be long, and usually are compound words from religious sources (derived from the names of Gods for Hindus, or from Arabic/Persian words for Muslims). Middle names can indicate place of birth, or origin. And of course caste may influence naming in Hindus.
I heard that the longest place name in the United States was the name of a small lake in Connecticut. In a native Algonquian language, it translates as “You-fish-on-your-side-I-fish-on-my-side-nobody-fish-in-the-middle.”
P.S., jaimest, the polysyllabic Hindu name I cited was a typical example of a Tamil name.
I heard there was a mountain or hill somewhere that’s name meant ‘Your finger, stupid’ - supposedly some explorer had learned the Native words for ‘What do you call this?’ and his guides misunderstood what he was talking about when he pointed at the mountain.
It sounds like a joke, but also like something that might actually have happened.
But you (deliberately?) forgot to explain what Mahalingam means in English.
Pratchett at his worst.
Guessing purely from a non-linguist standpoint:
Mahalingam
Maha=big Mahayana=Greater Vehicle (of Buddhism)
lingam=penis lingam=sacred phallic symbol
So Mahalingam means “Big penis”.
Almost but not quite. 
Lake Chargoggagoggmanchauggagoggchaubunagungamaugg is actually just over the border in Webster, MA.
Not all native American names are very long. “Chicago” comes from an indian (Pottawami, I believe) word meaning “stinking,” so I heard. Michigan is also an indian name, I believe meaning deep waters.
You are quite correct!
The Tantric religion of South India reveres the sacred symbolism of the sex organs as the divine love energy that gives life to all existence. Siva and Sakti, the masculine and feminine divinity united in eternal cosmic copulatory bliss.
Hey how come nobody mentioned Austin Power names like
felicity shagwell and Ivanna Humpalot
Because they were a poor imitation of Bond girl names. You can’t get much better than Pussy Galore (in Goldfinger).
Also, it has nothing to do with the topic of the thread, :wally .
It should be noted that the idea of a “name” (i.e., a traditional, meaningless (and therefore fairly quickly reduced to a couple of syllables) sound applied as a tag to a person) is something that only appears in the European[sup]1[/sup] tradition in the last millennium or so. Prior to that, short phrases were applied to pretty much everyone (the naming tradition of the Etruscans – picked up by the other Italic peoples – seems to be an exception; even most Roman cognomina and praenomina, however, are fairly transparent).
The same applies to Indian names, whether by “Indian” we mean “from the Americas” or “from the subcontinent”. For some reason, however, American Indian names are often translated into English.
[sup]1[/sup][sub]Defining “European” rather fuzzily, of course.[/sub]
So the Indian brave says, “In my tribe, we are named for the first thing the father sees when he opens the tent flap after the birth. That is why my younger twin is called Two Wet Dogs.”
“So, your name is Two Dogs Fighting?”
“Two Dogs Fighting? Ah, I would give the sun, the moon, and the stars to be named Two Dogs Fighting!”