In general it is a n-to-1 relationship, n >= 0. A symbol has always a name but it can have either no home package or one home package, and additionally there can be any number of packages in which it is accessible.
You have to think three-dimensionally ;) yes, two symbols with the same name in the same package are EQ. However, you can destructively alter packages so as to replace a symbol with another with the same name *at a later time*. Those won't be EQ, but a package will always contain at most one symbol with a given name - at a given time.

On Fri, Jul 3, 2015 at 2:52 PM, Scott McKay <swmckay@gmail.com> wrote:

On Fri, Jul 3, 2015 at 8:44 AM, Martin Simmons <martin@lispworks.com> wrote:
Packages are just a way to convert strings to symbols, which is useful when
they are obtained from files outside a running CL (e.g. via the reader/fasl
loader).

Agreed. Isn't it the case that {package x string} -> symbol is
a 1-to-1 relationship? In which case, two symbols having the
same name in the same package implies that the two symbols
are in fact EQ?

Sorry if I'm late to the party, I haven't been thinking about this
for a few years.

--S