Band gap engineering in hydrogen functionalized graphene is demonstrated by changing the symmetry of the functionalization structures. Small differences in hydrogen adsorbate binding energies on graphene on Ir(111) allow tailoring of highly periodic functionalization structures favoring one distinct region of the moiré supercell. Scanning tunneling microscopy and X-ray photoelectron spectroscopy measurements show that a highly periodic hydrogen functionalized graphene sheet can thus be prepared by controlling the sample temperature (T) during hydrogen functionalization. At deposition temperatures of T = 645 K and above, hydrogen adsorbs exclusively on the HCP regions of the graphene/Ir(111) moiré structure. This finding is rationalized in terms of a slight preference for hydrogen clusters in the HCP regions over the FCC regions, as found by density functional theory calculations. Angle-resolved photoemission spectroscopy measurements demonstrate that the preferential functionalization of just one region of the moiré supercell results in a band gap opening with very limited associated band broadening. Thus, hydrogenation at elevated sample temperatures provides a pathway to efficient band gap engineering in graphene via the selective functionalization of specific regions of the moiré structure.