Jon,
I've heard or seen them called cone tips and conical tips but I don't know what the "official" name is. All that I've ever seen screw onto the spout. All of the cans that I have with them were made by Eagle. One is the No 66, which has a straight spout and straight pump both sticking out of the side of the can. The tip is brass and the can is brass plated steel. The screw-on cap is plain (nothing attached to it). The second one that I have is probably painted as it looks more gold than brass. The spout and the pump are attached to the cap. The third is definitely painted, the cap is white plastic, and the can and tip are both cad or zinc plated steel. Tonight on eBay I saw several other variants. Not all have the cone tip. My second and third ones say Eagle but no number. Two numbers I've seen on eBay are 33 and 58. I bought the plastic capped one probably in the 1970's. The other two I got year before last off of eBay.
One other thing that the cone on the end of a taper is good for is lifting Gits oiler caps. Come to think of it, that's probably its purpose as otherwise, there's no need for the undercut just to use it on a ball oiler.
Robert D.