Is the Self Consistent Field an actual field? I know this is really stupid. But bear with me. 

In everything I have read so far, the Self Consistent Field (SCF) is always used to describe a method or a process, namely, that of iteratively solving the Schrodinger's Equation to generate new wavefunctions, using them for a new potential, and solving until convergence. 

If SCF is not an actual field, why is it named as such? And then when we describe the SCF space what are we really talking about? Does the iterative process create a series of objects that spans a field?

For SCF: https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method or if you want a textbook for reference, there's always Szabo and Ostlund's Modern Quantum Chemistry.
The notion of a self-consistent field comes from the orbital approximation - that a multi-electron wavefunction can be approximated as multiple one-electron wavefunctions.

At that point, the question remains - how does each of those electrons interact with the remaining $N-1$ electrons?

Well, there's an electric field from the electron density, right? Maybe you want to call this an electrostatic potential -- but Hartree considered it a spherically-symmetric electric field.

The problem, of course, is that since you don't know the final charge density, you have to make a guess and iterate until it's "self consistent."

Thus, SCF has been associated first with HF theory, and other related methods, including Kohn-Sham DFT.