It's not a leatherworking tool or a tap and die tool. I don't own it and scraped the pic off of the internet so I don't know the overall length. For scale, I would assume the wooden "bulb" fits inside of the average palm/hand.
It's some kind of extraction tool, but it is not used in dentistry. (And I wouldn't want to extract from your dentist, for the record.)
A small bearing puller or seal extractor what ever it is extracting must fit onto something cause of the center punch.