There's nothing you can do to repair the damage - that's up to the tree. Do NOT cover the damaged area with anything! Leave the damaged area untouched and open to the sun and air. The tree will callus over and in a few years only a light scar will remain. If the damage has not gone too deep (and I really think it hasn't), then your tree will recover on its own.
Right now, the buds seem to me to be swelling. If this is the case, then your tree has not been girdled and will live, although some branches may die back. If I'm wrong and the buds are still dormant, then you'll know within a month or two if the tree has been girdled because the new leaves will not open entirely and the tree will rapidly die.
Many trees can recover from as much as 75% or more damage to a trunk, but this is IIRC species dependent (I once owned a chokecherry that was severely damaged by a deer - it had removed at least 85% of the bark and cambium - and the tree recovered).
As for tree identification, it kind of resembles a Serviceberry (Amelanchier species), although the structure may be incorrect for serviceberry. Flowers would really be a definitive ID marker.