I was puzzled for years over why the word “modern” served as any description of anything- what does it tell us except that it is held by people now existing? St. Thomas even refers to himself as “modern” (cf. Proemium to the Commentary on Divine Names).
In its present sense (modern sense?) the via moderna first referred to the philosophy of William of Ockham. There is no agreement on even what to call the philosophy of Ockham beyond that it is the origin of the via moderna. It is pretty clear that the name “nominalism” was imposed on his thought by his adversaries. This is not to say that the word fails to be an apt description (a description of a doctrine is not necessarily wrong for being imposed by an opponent) it is only to say that the disagreements about Ockham’s thought are so profound that they reach even down to the name that we should call it- with one exception. Everyone agrees (for the moment) that it should be called the modern way as opposed to the ancient way.