The following explanation was posted to the SPSS-X list a few years ago:

For some historical clarification on the term SPSS as used for the software package (as opposed to the company), the original name was indeed Statistical Package for the Social Sciences. When what was to be Release 10 of that package was released in about 1983, the name was changed to simply SPSS-X (actually, the X was a superscript). I have seen nothing in any SPSS materials dated later than the early 1980s that have referred to it as Statistical Package for the Social Sciences or anything other than just SPSS-X. With Release 4.0, it became just SPSS. There was also SPSS/PC+ for DOS, and now of course SPSS for Windows, the first release of which was 5.0. So my understanding is that the term SPSS as applied to the company means Statistical Product and Service Solutions. As applied to the product or package SPSS, it now just means SPSS. - David Nichols, Principal Support Statistician and Manager of Statistical Support, SPSS Inc.