Wikipedia has this enigmatic sentence on the page for the fundamental theorem of algebra:
...its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.
While it sounds plausible, it begs the question:
Question: In which time period did the title "fundamental theorem of algebra" get assigned to this theorem? And who were the main contributors to this title?
Searching MathSciNet for "fundamental theorem of algebra" revealed:
Bôcher, Maxime; Gauss's third proof of the fundamental theorem of algebra. Bull. Amer. Math. Soc. 1 (1895), no. 8, 205–209, MR1557382.
And by a Google Scholar search, I found this article, which mentions it in passing:
William E. Story, A New Method in Analytic Geometry, Amer. J. Math. 9, (1886), pp. 38-44.
However, it seems unlikely that these are the earliest references.