We use density-functional theory with a Hubbard correction to investigate Ti-centered electron polarons at neutral PbO-centered ${180}^{\circ }$ domain walls in tetragonal . The Hubbard parameter for Ti $3d$ states is determined using the finite-size-corrected polaronic energy-level alignment procedure, yielding stable electron-polaron formation in bulk PbTiO${}_3$ with a trapping energy of $-$0.06eV.Inthedomain-wallsupercell,theexcesselectronlocalizesonaTisiteandformsaTi$^{3+}$ center with an occupied in-gap $d_{xy}$ state. Comparison of bulk-like and near-wall Ti sites shows that their trapping energies differ by only about 0.01 eV, indicating that this neutral domain wall does not provide a significant thermodynamic driving force for electron-polaron segregation. While the Ising-like reversal of the out-of-plane polarization is preserved, the localized electron induces a finite transverse polarization component normal to the wall, enhancing a local N'eel-like distortion that is strongest when the polaron is located at the wall. These results show that neutral ${180}^{\circ }$ domain walls in PbTiO${}_3$ do not substantially alter the stability of Ti-centered electron polarons, but they can couple to the polaron-induced lattice distortion through a localized transverse polarization response.