The photon is the quantum of EM energy (field). What is the name of the energy fields of the rest of the fundamental particles? ( I.E. the up quark, down quark, electron etc.)
Fermions don't produce fields in the same way that bosons do, because they obey Fermi-Dirac statistics, rather than Bose-Einstein statistics. Strictly speaking, the electron is the quantum of an "electron field", each quark is the quantum of its own "quark field", etc.
These fields don't do much, however, because the particles that mediate them can't multiply in an unlimited sense (see Pauli's exclusion principle.)
All of the fundamental bosons, however, have their own fields: W's and Z's are the quanta of the charged and neutral weak fields, respectively, the gluons of the color fields, and there's the special "Higgs field", which is a whole nother animal, because the Higgs has a non-zero vacuum expectation value (vev).