I'm assuming the namespace is the allotted place in memory in which the name is to be stored. Or are they the same thing?

A namespace is a theoretical space in which the link between names and objects are situated: that is what is called a mapping between the names and the objects.
Names are the identifiers written in a script.
Objects are structures of bits lying in the memory.
The data structure that implements this theoretical namespace is a dictionnary. "Implements" means that it is the object that holds this data in the bits of the memory.
But the objects that this dictionary references are not grouped all together in a delimited portion of the memory, they are lying everywhere in the memory, it's the role of the dictionary to know how to find any of them with just a name at start when a name is encountered by the interpreter.
That's why I wrote it is a theoretical space, though it has a concrete existence in the memory. It is theoretical because the fact that several objects disseminated at different places in the memory can be considered to belong to one namespace is the result of the under-the-hood functionning of the Python interpreter, that is to say its data model and its execution model

In fact, things are more complex, under the hood there is a symbol table in the game. But I'm not enough competent concerning the C implementation of Python to say more. And by the way, people rarely allude to the symbol table.

However, I hope that the above explanation will shed some light in your mind concerning the subject of namespace.