In the lambda calculus, are there commonly accepted names for $x$ and $M$ when they appear in $\lambda x [M]$ ? Something along the lines of "binder" and "bindee"?
$x$ is a "bound variable" and $M$ is the "scope" in which it is bound.
In logic the $\phi$ in $\forall x . \phi$ is called the matrix, and $x$ the bound variable and $\forall x$ the quantifier. By this analogy I would call $M$ in $\lambda x . M$ the matrix, $x$ is the bound variable, and $\lambda x$ is the abstraction, or maybe the "abstractor"?