I suspect part of the reason is to distinguish the profession of surgery from its predecessors.
Apparently the earliest surgeons trained as barbers, and of course they had the sharp implements necessary to cut people open, remove limbs, and so on. This was a painful and bloody business with, unsurprisingly, a low survival rate.
As modern surgery developed, those who were medically trained would want to make it clear that they had no connection with the old ways, so a renaming of their kit is one way to show this to patients.
It probably helps reduce patient anxiety. Someone approaching me with a saw is scary, but if I'm told that an osteotome will be used in the operation I'll feel a lot happier about it