It looks like OpenOffice.org 1.01 was released while I had my back turned ;). And, yes, the official name of this MS-Office-like product is indeed “OpenOffice.org”.
For those not aware, OpenOffice.org is a great free software package that includes a word processor, spreadsheet app, and presentation app (just like the Office you’re used to). It’s available for Windows, Linux, and Max OSX.