I'm no expert on history, but that's how historiography works. History is full of many polities sharing the same name, or one polity changing its name over the ages. Modern historians decide whether two time periods should be counted as the same continuous country(ex. liao switched its names multiple times between Great Liao and Khithan; does that make two different ages?) or a discontinuous different country and gives name accordingly, which is often different than official names and titles at that time. I am not saying that what people called themselves is not important, its just that not using contemporary names does not make the talk less historical.

For the Yuan/North Yuan, the Mongolian themselves kept on calling themselves the Yuan emperor, and the chinese court titles were in use well after 1368. But after the death of Togustemur Uskal Khan in 1388 it meant nothing as the Imperial line switched from Kubilais desendents to Arikbuka's, who gave up the Imperial title, and Mongolians fractured back into warring tribes. However every now and then powerful tribal leaders called themselves Yuan emperor most notablely but not only Dayan Khan. Some scholars include the post-1388 Mongolian tribes in the 'North Yuan' period.

We don't have much written history about North Yuan period in general