Wikipedia:

In late 2006, programmer Jed McCaleb thought of building a website for users of the Magic: The Gathering Online tradable card game service, to let them trade "Magic: The Gathering Online" cards like stocks.[13][14][4] In January 2007, he purchased the domain name mtgox.com, short for "Magic: The Gathering Online eXchange".[15][16][17][18] Initially in beta release,[19] sometime around late 2007, the service went live for approximately three months before McCaleb moved on to other projects, having decided it was not worth his time. In 2009, he reused the domain name to advertise his card game The Far Wilds.[20]

In July 2010, McCaleb read about bitcoin on Slashdot,[21] and decided that the bitcoin community needed an exchange for trading bitcoin and regular currencies. On 18 July, Mt. Gox launched its exchange and price quoting service deploying it on the spare mtgox.com domain name.[14][22]

I'm not sure when people started to refer to it as Mt Gox.