I think the anchovies are what gives the Pasta Puttanesca its name.
We made it once. Didn’t like it enough to make it again.
-JT
The entire point is to make a dish that is quick, salty, and filling. Olives, capers and/or anchovies certainly fill the bill here.
The 'puttanesca' derives from 'puttanata' (stuff; garbage; something worthless), as supposedly originally conceived by the restauranteur Sandro Petti in the 1940s or 1950s at his place in Ischia. The tales about ladies of the evening don't really hold water, but are entertaining stories.