Parents aren't given names of kids that have bitten, hit etc. by other kids becuase what tends to happen with some kids is that they can become labelled as 'naughty' kids by some parents and some parents tell their kids to actually avoid them. With young children, I think that instead of avoiding, we as teachers need to give/show the kids what good behaviour is about. As parents it is very upsetting (I have struggled with my teacher and parent of a toddler hat) but lot of hitting etc. is part and parcel of being a toddler as they stuggler to find their feet and independence. Alot of these incidents happen when kids want the same toy so as a teacher I try to instill a good sense of sharing, and make sure that each child knows that even if they don't get to play with a toy first, that they WILL have a turn. Kids usually work things out and become friends again. We also have a daily circle time where we talk about good behaviour and how we can be kind to be eachother.
In my first year of nursery teaching, I had a few really nasty parents who would actually say really mean things about some of the kids in the class. Some kids would say, 'my mum saids you're mean and I shouldn't play with you', which was so sad. The kids who were saying mean things as a result of waht their parents had said to them, were in my opinion, harder to 'reach' than the kids who would naturally and instinctively hit out if they wanted something.
I think that the parents of children who hurt others, SHOULD however be informed that they have hurt another child so that they can be kept in check of how their child is doing developmentally and know how they and I can support the child's learning and physical and social development. Sometimes as we all know, these incidents are one offs and other times, not so.
At my child's nursery, a child scratched him so badly that he still has a scar(now faint but still there) over a year later. When I asked if the parent had be informed they said no. I was very angry as the child's nails must have been very long to make such a tear. In the end, the nursery decided to change the policy and inform parents and needless to say they said that the child's nails had indeed been very long!
I would say that if incidents persist, rather than asking who the child is, ask if the incidents have involved the same child and if so ask how the nursery plans to avoid these accidents happening. Maybe they could monitor the child very carefully and redirect him or her before any other accidents are likely to occur.
Sorry for the long post! It is a hard and emotional issue.