Why is lambda calculus named after that specific Greek letter? Why not “rho calculus”, for example? Where does the choice of the Greek letter $\lambda$ in the name of “lambda calculus” come from? Why isn't it, for example, “rho calculus”?

I heard that Church originally used the hat symbol above the bounded variable, like $\hat x.x$, in handwritten papers. Then, the notation became ^x.x because of old-fashioned typewriters. I think it first became $\Lambda x.x$ when more recent text processors appeared, and $\lambda x.x$ after that (for aesthetics reasons probably).
Thanks to the silent downvoter, I did some googling and found Barendregt version in “The Impact of the Lambda Calculus in Logic and Computer Science”:

We end this introduction by telling what seems to be the story how the letter 'λ' was chosen to denote function abstraction. In [100] Principia Mathematica the notation for the function $f$ with $f(x) = 2x + 1$ is $2 \hat x + 1$. Church originally intended to use the notation $\hat x.2x + 1$. The typesetter could not position the hat on top of the $x$ and placed it in front of it, resulting in $\wedge x.2x + 1$. Then another typesetter changed it into $\lambda x.2x + 1$.

