This style I've called a "School Pen" in my proposed "Pen Shapes" glossary.
https://thesteelpen.com/2018/12/07/pen-shapes-a-proposed-glossary/Mainly I use this term because the 404, and then Esterbrook's copy, the 444, as well as Hunt's version are all, at one time or another, called School Pens. Miller Brothers also made one, as well as Eagle, and they also used the term School Pen. I suspect the ridge was there to ensure the student didn't push the pen point too far into the holder. But that's just a theory.
Here's Esterbrook's copy of the Gillott. (Esterbrook initially called their copies 303 and 404 until they were sued by Gillott, after which Esterbrook changed the name to the VERY DIFFERENT 333 and 444. I've also attached one of the 404s still being used in a salesman's sample book where it is labeled as a 444. This example is from the early 1870s, not too long after Esterbrook lost the lawsuit.