Why do we use $\Gamma$ to denote a TM's tape alphabet?
Following up on @PartialOrder's comment, while $\Gamma$ is not used in Chomsky &amp; Schutzenberger or in Chomsky's 1962/1963 papers on PDAs, it is used in Ginsburg and Greibach 1966 as follows:


  A pushdown automaton (abbreviated pda) is a 7-tuple $M=(K,\Sigma,\Gamma, \delta, Z_0, q_0, F)$ where [...]


Here $K$ is the set of states and $q_0$ is the start state. $\Gamma$ is the finite nonempty set of auxiliary symbols. $F$ is the set of final states. $\Sigma$ is the finite nonempty set of inputs. Etc.

Nowadays we would call the set of states $Q$ if the start state is called $q_0$. I think this just indicates that not too much consistency and reason was required for these letter choices.

This is "original research" but I figure $\Gamma$ may just have been used since it is the first capital Greek letter (to indicate the same type as $\Sigma$) which looks distinctly greek (A and B looking Roman as well).