I'd go back to the teacher and say that though they may not be seeing anything your DS is still telling you this is happening, so can the playground staff (will probably be lunch time supervisors or TAs, but might be teachers) keep a look out.
How I go about it from there would depend on how upset your DS is and whether he can process the idea that what this child is saying says more about them than it does about him, along the lines of "People who have to boast all the time must be very sad and sometimes when people are sad they feel like they have to make other people sad to make themselves feel better. It isn't very nice, but it doesn't make you any less brilliant at [insert whatever it is he's good at] so try and ignore him". Really bolster your DS with specific praise about everything he's doing well.
I would also keep a note of what DS says and when he says it, but not in front of him, so if the school comes back with nothing, or if it gets any worse you can give them some examples.
The school should have a bullying policy, check their website and any literature you got when he started and see what it says.
Do be prepared for the possibility that there are two sides to the story, it doesn't sound like it from your posts but sometimes children leave out the fact that they thumped someone right before the thumped child called them names.
Good luck, it may take a little while to resolve so try and keep your DS positive if you can.