What's the name of the tool to bevel bar ends? I noticed the mechanic at my LBS used a tool to smooth out and bevel the end of the steering tube after cutting it. It looks like a useful tool to smooth out the edge of bar ends as well. It's round and has a cone inside, what is it called? I don't have a picture unfortunately.

When the tubing is cut the cutting tool leaves a ridge in the inside of the tube. A reamer removes this rough edge or burr. It is hard to say if your mechanic used a bicycle specific reamer which may be part of a bearing facing tool or a generic deburring tool.