PyPy dates to 2007 (older than Pip!); back then I'm pretty sure people were still calling PyPI the Cheeseshop, and it was still hosted on the main python.org site for years after that (https://packaging.python.org/en/latest/guides/migrating-to-p...).
Not to mention that the PyPy name was established long before the initial release too. It was in development at least since 2003, under that name.
IIRC there was a PyPy talk at EuroPython 2003.
The first commit to the current repo is dated Feb 24, 2003, and the commit message is:
Move the pypy trunk into its own top level directory so the path names
stay constant.
In the next episode of Complaining About Names; Why did those silly South Americans give their forest the same name as Bezos' company? :-)