  We construct composite and partially composite Higgs models with complex
pseudo-Nambu--Goldstone (pNGB) dark matter states from four-dimensional
gauge-Yukawa theories with strongly interacting fermions. The fermions are
partially gauged under the electroweak symmetry, and the dynamical electroweak
symmetry breaking sector is minimal.
  The pNGB dark matter particle is stable due to a $\mathrm{U}(1)$
technibaryon-like symmetry, also present in the technicolor limit of the
models. However, the relic density is particle anti-particle symmetric and due
to thermal freeze-out as opposed to the technicolor limit where it is typically
due to an asymmetry.
  The pNGB Higgs is composite or partially composite depending on the origin of
the Standard Model fermion masses, which impacts the dark matter phenomenology.
We illustrate the important features with a model example invariant under an
SU(4)$\times$ SU(2) $\times$ $\mathrm{U}(1)$ global symmetry.
