The genus $g$ Torelli group $I_g$ is the kernel of the action of the mapping class group of a genus $g$ surface on the first homology group of the surface.
The first paper I am aware of that uses the name "Torelli group" for this group is
Johnson, Dennis A survey of the Torelli group. Low-dimensional topology (San Francisco, Calif., 1981), 165–179, Contemp. Math., 20, Amer. Math. Soc., Providence, RI, 1983. (Reviewer: J. S. Birman) 57N05 (14H15 32G15 57-02)
It had previously been studied without this name in numerous papers (e.g. earlier papers of Johnson, work of Powell, and work of Birman-Craggs). In Johnson's survey above, he says "The topologists had no name for it, but it has been known for a long time to the analysts, so I will use their label: the Torelli group".
Now, I understand the mathematical justification for calling it the Torelli group, namely Torelli's theorem. My question is instead historical : Johnson's sentence above seems to imply that he did not make up this name, and thus that there are older papers (maybe by analysts or algebraic geometers?) that use it. Is anyone aware of any?