In Spectra of graphs: theory and application, Dragoš M. Cvetković, Michael Doob, Horst Sachs, pg. 52, Section 2.1 "The polynomial of a Graph", it's called product and denoted $G_1\cdot G_2$.

I would hesitate to call it composition, lest it is confused with the lexicographic product, which is, however, denoted $G_1[G_2]$ in the reference above.

Edit: maybe, to distinguish it from other products, call it "matrix product of graphs"?