The second paragraph of Plotkin's 1973 Memo on Lambda-definability and Logical Relations says this:
"The definition of logical [relation] is derived from a corresponding
one of M. Gordon for the typed λ-calculus."
This doesn't say explicitly that the term was coined by Gordon. But, given that the memo is titled "Lambda-definability and logical relations" as if "logical relation" is an already known idea, and the second para says "construct certain, so-called, logical relations," I think it very likely that Gordon coined the term and Plotkin used it hence. (Plotkin confirmed to me that whatever he wrote in the memo is correct.)
Gordon is credited again at the top of p. 12,
"M. Gordon proposed, as a possible remedy, that relations... should be
extended - not just permutations."
The published version of the paper ("Lambda-definability in the full type hierarchy" in To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism) has this remark. It also has a remark that could be construed as an explanation of the term "logical relation":
Because of the "logical" nature of the $\lambda$-definable elements, they should be invariant under permutations of $D$.
In my view, this is an extremely satisfying explanation of why logical relations are "logical". Lambda calculus is logical and, so, the functions defined using it will be uniform with respect to the base types. They can't "see" the permutations we might do to the values of the base types. Viewed in this way, what Gordon and Plotkin meant by "logical" is essentially the same as what Reynolds calls "parametric".
However, the term "logical relation" doesn't appear in the published version of the paper. It is possible that the referees might have objected that the term was confusing and Plotkin might have decided it best to avoid the term. But, Statman went back to the old terminology and the term has come back into popular parlance.