You know the conical end of a ballpoint pen that holds the ball inside the end of the conical shaped end of the ballpoint? Is there a name for the conical end? I am thinking it has a name, but I never learned what the name was. Does it also come with several names? If it's the case, what are they?
Colloquially I'd call that the tip of the pen. There may be a technical term for it, but that's a question for a different StackExchange site.
From Merriam-Websters's definition of ballpoint pen:
: a pen having as the writing point a small rotating metal ball that inks itself by contact with an inner magazine
Note that the definition uses the phrase writing point, which makes sense. So, really, the end of a ballpoint pen is its point.