It's actually M. T. Gox, named for Martin Theodore Gox, the famous 19th century industrialist who once sought to increase his wealth by buying up tungsten after it was found that tungsten was useful in the manufacturing of the then-new invention of incandescent light bulbs.
At one point, Gox owned 90% of the marketable tungsten available to North America. However, tungsten didn't take off until decades later. Edison, the most famous researcher of light bulbs, used a carbon filaments in mass production even though it was inferior to tungsten and other metals. Some say that M.T. Gox shot himself in the foot because Edison's decision to use carbon was in part due to Gox cornering the tungsten market and pissing off Edison. However, there was bad blood between the two for other reasons, such as Gox stealing away with a woman that Edison loved. M.T. Gox was tall, barrel-chested, and with an impressively large mustache. Edison claimed that Gox only won the woman by inspiring her lust rather than involving charm, personality, or love.
Mr. Gox lost much of his fortune as he started to sell off his metals. He had invested in other semi-rare metals as well that were used in new electrical technologies, but tungsten hurt him the worst. In order to facilitate getting the maximum amount of of money for his devalued tungsten, he set up an exchange. It was the first non-physical exchange of it's kind, which was necessary because tungsten, aside from light bulbs, did not have a centralized industry. He could saturate the New York region in a single day of selling only a mere fraction of his metal stores. So, he needed to sell all over the world so as not to ruin local markets.
But moving metals around the world is a costly problem. Instead, he funded a third party to keep the store and issue contracts. These contracts were some of the first examples of a widely-traded commodities "forward contract" system. However, mailing contracts was too slow for an exchange, so he hired William Bacon, a mathematician and cryptographer, to devise a system in which a buyer and seller could make an agreement over telegraph such that they were ensured of one another identities, that the money and contracts had actually been transmitted, and that no man-in-the middle could impersonate or take advantage of either party.
The contracts themselves were not necessary at that point. A buyer would telegraph Gox's exchange to initiate and confirm IDs, then make a deposit at a Gox-owned account at a local bank and be given unique amount and time-specific cypher instructions by the banker. Then Gox associates would telegraph a similar cypher. At a later date, when the buyer or those in his employ wished to obtain the physical tungsten, they would present their contract at the warehouse. But since most were presenting their transaction credentials to obtain contracts just before turning them in at the same place, Gox did away with the paper contracts entirely. People just walked up, wrote down numbers, passed it over to the clerk, and the tungsten was traded.
The transaction credentials mentioned above included an encrypted message from the bank, the seller, the buyer, and the originator (the exchange). Pretty soon, however, people figured that they could sell their contracts to another party just as long as that transaction was added to the sequence. For each sale, the exchange also verified the prior transactions in the chain and added an encrypted message saying as such. Some of these chains grew to hundreds of exchanges long, including thousands of digits that pissed off telegraph companies until the first mechanical tickers were invented to speed the process.
However, the exchange was doomed as it was robbed of much of its metal stores over the course of weeks by a cabal of employees. This was kept secret, however, as Gox had made the exchange a third party, thus removing himself from liability, and he postulated that "we only need access to a fraction of the contracted tungsten at any one point in time." Some say that Gox paid these employees to rob the metals so he could sell them a second time. Indeed, for the years after the robbery, Gox deposited more and more into the exchange, declaring it was coming from a questionable personal warehouse or dubious refineries.
This came to an end when a mysterious individual showed up at the exchange and presented transaction credentials for a large amount of tungsten. Then, another mysterious individual did the same. And again and again until the tungsten was nearly gone and legitimate traders made a run on the exchange. Well, actually, they tried to make a run but a traffic jam developed on the roads to the warehouse, along with other insanely coincidental transportation problems such as Sheriff closing two bridges under claims of structural damage and a rancher blocking a road with hundreds of escaped cattle. This real-life "distributed denial of service" continued until these mysterious strangers were able to complete their trades.
Gox believed that Edison had cracked William Bacon's encryption and paid employees to take tungsten with phony contracts. That's where the phrase "phony contracts" came from, as they were some of the first popular contracts transacted over the telephone rather than by wire.
Soon after, Edison practically confirmed these suspicions by developing and mass-producing a tungsten-based light bulb and his company never seemed to actually purchase tungsten from any outside source. In 1996, chemists studied multiple samples and were able to confirm that, indeed, Edison's tungsten had come from the Gox exchange and were part of its latest stores.
Anyway, MTGox.com, the website, was thus named in honor of the man who invented the first electronic exchange. It seems quite apt considering the eerie similarities to the 1800s Gox exchange and it's basis on a sort of cryptology-dependent currency.