Labels have uses; they are there to enable us to refer to specific things without lengthy descriptive sentences. It is, I think useful to be able to refer to Justus Lipsius, Guillaume Du Vair, and others in a way that distinguishes them from either the ancient Stoics, or their contemporary Christians.

If we follow thic logic we should talk about "Neo"-chemistry or "Neo"-physics which is likewise absurd. Same with Stoicism. All the prefixes like "neo", "ultra", "modern" are based on a profound lack of knowledge (and even worse: half-knowledge) about the system and/or a desire for fame.

If we were referring to them as neophilosophers, this analogy might hold. By this logic, though, we should be referring to Buddhism, Existentialism, Objectivism, etc. as "Stoicism" as well. The term "Stoicism" as it is used now, though, is useful as a something other than a trivial synonym for "philosophy"; it refers to a specific set of philosophers and their body of teachings.

Lipsius and his compatriots likewise form a group to which it is useful to refer. Their philosophy was distinct form others of their time due to a greater influence by the ancient Stoics, but it was certainly not the same philosophy as the ancient Stoics. From the perspective of those that originally gave them the name (John Calvin in 1536, according to this article), what distinguished them from their contemporaries were elements drawn from Stoicism. It (their philosophy) was clearly not the same as ancient Stoicism, specifically because it much closer to contemporary (to John Calvin) philosophy and religion, hence the name neostoicism.

The name "neostoicism" has since been used to refer to the views of Lipsius et al. for nearly 500 years. Changing the name we use to refer to them would do nothing but stir up confusion.