name of Squaresoft
Square Co. Ltd. began as a sub-division of the Den-yu electronics company of Yokohama in third-qurter 1983. Their first game was completed in Fall of 1984, and by Summer 1985 a license to develop from Nintendo was aquired. Less than optimal sales promted the division to be let loose in September of 1986, when they officially became Square Co. LTD.
After a few failing games the Executive Producer, Hironobu Sakaguchi, decided to take one last gamble. Devoting most of the fledgling company's development resources into a single project, Final Fantasy1 was released on December 18, 1987 in Japan, and sold like hotcakes. It turned the company around forever, and insured them a geek household name.
Square Co. Ltd. became 'Squaresoft' to american gamers in 1989, when Square created Squaresoft Inc. in Redmond, Washington. In present day, the parent company seems to be referring to itself as Squaresoft as well, but that may be skewed by this noder's Americocentric viewpoint2.
1Called Final Fantasy because it was to be Hironobu's last game. However, the game was such a success that they continued the franchise, and the name stuck, making Final Fantasy a success, as well as no-so-Final ;)
2Which is to say I don't see how they refer to themselves in Nippon, but after an extensive search, I can't seem to find any references on the web about Square Co. Ltd. past the early 90's.