What is the history behind the name that we gave to that class of galaxies?
The term can be traced back to the theoretical work of C.C.Lin in explaining the spirals as due to density waves in galactic discs.
A paper from 1970 discusses the "Existence of 'Grand Design'". Note the use of "scare quotes", suggesting that the term was new and would not be widely recognised by his readers.
Chia-Chiao Lin was an important Chinese/American Mathematician. It is reasonable to believe that the term was coined by him or one of the mathematicians that he worked with at MIT. And was in use since about 1964, when the first of a series of papers "On the structure of Spiral Galaxies" was published.