There is no deep explanation for why CADi is so named.
CADi
is merely a nice short word with a Z in it,
that had not previously been used in this context.
The CAD prefix suggests a not entirely inappropriate application domain,
and hence the acronymic deriviation
Computer Aided Design in Z,
though application of CADi
is clearly not limited to that domain.
That prefix also led to the mixed-case rendering of the name,
which seemed to be trendy at the time.
In the very early days, before the name CADi was thought of,
the Z typechecker was known as Zork.
This was a contraction of Z from York.
However, that name was associated by some people with a certain computer game,
and so we stopped using it.