The name is an allusion to SheepShaver Shapeshifter, the 68K - Macintosh emulator for the Amiga.
Together with parts of the program code of Basilisk II, SheepShaver was created for BeOS in 1998, first as shareware, later as part of BeDepot. In order to be able to emulate newer versions of Mac OS, a PowerPC emulator was required. The last Mac OS to support this computer architecture is Mac OS 8.1. Since Shapeshifter and its further Basilisk II than 68k - Macintosh are designed emulator can use it only Mac OS run as guest operating systems for 68k Macintosh computers.