I happen to own
History of Analytic Geometry
by Carl Boyer, who says on page 179
Maria Agnesi first plotted it from the equation (which Fermat
had given more than a century earlier) . . .
In footnote 41 on the same page
The name "witch," customarily used in English, apparently is due
to a mistranslation. The word "versiera" which Grandi coined in
1718 to indicate the manner in which the curve is generated, has
also the meaning "witch" in Italian, but this has no connection
with what Grandi and Agnesi had in mind. See Gino Loria
Spezielle algebraische und transcendente ebene Kurven
(Leipzig, 1902), page 75.
On the origin and properties of this . . . and also for
numerous bibliographic references to sources, the work of Loria
is most valuable. See also R. C. Spencer,
Properties of the Witch of Agnesi,
Journal of the Optical Society of America, XXX (1940) p. 415-419.
Best wishes,
Sam Kutler