I am aware of some of the history of the gamma function $\Gamma(z)$, partly through a 2009(!) MO question "Who invented the gamma function?"—Euler, Bernoulli, etc. My question does not seem to be answered in that discussion, or in other historical accountings I can easily locate:
Q. Why was the symbol $\Gamma$ chosen for the generalized factorial?
Were $\alpha(z)$ and $\beta(z)$ already "taken" and so $\Gamma$ was a natural successor? Or was the choice due to the shape of the uppercase $\Gamma$? Or some other reason? Or lost to history?