Haydn and nicknames, it is a thing: the opus 55 no 2 here was named Razor, and it was part of a six part cycle called Tost. That name was taken from Johann Tost, a violinist in the Esterhazy orchestra where Haydn worked. But where is that razor coming from?
The name was not given by Haydn, but appeared later, from the 19th century onwards. There is an apocryphal story that describes Haydn selling his string quartet for a beautiful razor. Highly unlikely, because rich mister Haydn didn’t have a reason to sell anything. He was doing very well for himself. A musical reason might be the sharp introduction on the violin at the start of the work.
The Salomon Quartet has recorded all of Haydn’s quartet (a considerable feat!) on period instruments and using baroque phrasing. For me it is the only way I can listen to them. Haydn’s famous series has been performed in the past as if it were a symphony, but that way you miss the open, classical nature of these works.