Woodchuck is another name for the ground hog. As for shooting one in the back yard, that depends on where said yard is located. If it's in a municipality, you can't shoot there in the first place. (Some places have made shooting a bow within the municipality illegal.)
However, if your back yard is measured in hectares or acres and you make your living from it, then you can shoot the 'chuck. Assuming there are no local by-laws about discharging a firearm. However, you cannot hunt, even on your own recreational dirt, without a small game licence.