Michelle Francl in Nature Chemistry is making a case for named reactions. It is interesting to read the habit of naming reaction is relatively new. Those long-dead nineteenth century Germans did not start the habit! It is also good to see Wikipedia cited for once. The article links to the List of Organic Reactions most of which are indeed named after contributing scientists.
But why do chemists use named reactions? Francl mentions it is a way to honour discoverers, it teaches some history behind the invention to students and it makes it easier to find relevant literature. There are disadvantages: other discoveries by the discoverer are obscured and it makes it harder to study a particular field.
Somehow systematic naming of chemical reactions has never made it. But is there another more scientific way to name reactions or rather protocols? In an ideal world the name of the protocol should always lead to the relevant publication. Naming the protocol to all contributing authors and not just of few would then be acceptable. And why not naming it after the journal. The Wittig reaction could also be known as alkylidene-de-oxo-bisubstitution (systematic, see March) or as the Wittig-Schollkopf reaction (use all authors even if it is just the assistant) or as the CHEMBER19541318 protocol.

PS. The most recent named organic reaction in the list is the Bingel reaction (1993). In the past 20 years what have been the top-10 ground breaking new protocols and if not a named reaction what are they then called? Hopefully not something like aproticphotochemicalenentioselectivereagentAmediatedfunctionalgroupBtofunctionalgroupCconversion