
Figure 1. Subset of the LRT focusing on the rabbit/rodent and kin clade where gophers nest with hedgehogs.
In the large reptile tree (LRT, 1258 taxa, Fig. 1) the naked mole rat (genus: Heterocephalus, Fig. 2) nests with the hedgehog clade, one node off from the mouse/rat/clade. So the naked mole rat should be the naked mole gopher.

Figure 2. The naked mole rat, Heterocephalus is closer to hedgehogs than to rats.
Heterocephalus glaber (Rüppell 1842-5; 8-10cm) is the extant naked mole rat. It has a cold-blooded metabolism, lives underground, and can move backwards as fast as forward. Not the claws, but the teeth (protruding outside the lips) are used for digging. Heterocephalus is essentially hairless, lives in a colony dominated by a queen and may live up to 32 years in a low oxygen environment, or several times longer than related taxa.

Figure 2. Naked mole rat (Heterocephalus) skull in several view. The mandibles are disarticulated here, but the glenoid appears to be reduced to absent, providing great mobility to the jaws.
Ceratogaulus hatcheri is the extinct horned gopher (Fig. 3). It nests with the naked mole rat in the LRT (Fig. 1).

Figure 3. Ceratogaulus, the extinct horned gopher
Thomomys bottae (Figs. 4, 5) is the extant pocket gopher, another rodent nesting with hedgehogs.

Figure 4. Skull of Thomomys, the extant pocket gopher. No large retroarticular process here.
These taxa look like rodents
but they nest with hedgehogs. So do we expand our concept of rodents (lumping)? Or make new clades (splitting)?

Figure 5. Skeleton of Thomomys, the pocket gopher.
Rodentia is characterized by a single pair of continuously growing incisors in each of the jaws, as opposed to rabbits, which have two incisors.
Glires (Latin glīrēs, dormice) is a clade consisting of rodents and lagomorphs (rabbits, hares, and pikas). In the LRT many more clades of small mammals nest with rabbits and rodents.
Euarchontoglires (synonymous with Supraprimates) is a clade of mammals, the living members of which belong to one of the five following groups: rodents, lagomorphs, treeshrews, colugos and primates. In the LRT rodents nest with primates, but not colugos.
References
Rüppell E 1842-5. Säugethiere aus der Ordnung der Nager, beobachtet im nordöstlichen Africa. Museum Senckenbergianum: Abhandlungen aus dem Gebiete der beschreibenden Naturgeschichte. 3: 99–101.
wiki/Hedgehogs
wiki/Erinaceus
wiki/Echinops
wiki/Naked_mole-rat