I likewise have needed such a thing—to converse coherently about transformation properties (actually symmetries) of power, exponential, and logarithmic functions. I did not find anything in textbooks or anything commonly used otherwise. I considered using $\rho$ for "ratio", but settled on $\sigma$ (and  $\sigma_y$ as needed), because in conversing, "scaling" was more used than "ratio." Following are examples of summary statements.

An exponential function $f(x) = A b^x$ scales by the same factor over equal increments of the input. The base $b$ gives the factor over a unit increment.
The base to the power of an input increment $\Delta x$ gives the output factor: $$\sigma_y = b^{\Delta x}.$$
The graph is invariant under the family of transformations
$$(x,y) \rightarrow (x + \Delta, b^\Delta y)$$
where $\Delta$ is any real number.

We use $\Delta x$, but "$\sigma y$" is clumsy, so I use a subscript. I try to avoid the subscript. I would write the transformation property ("equivariance") of the function as
$$f(x + \Delta) = b^\Delta f(x),$$
provided students were ready for such symbolic stuff. (Usually some are, some aren't—a chance to "differentiate" instruction.) In making tables of values, often a column would be labeled with a $\sigma_y$ (or $\sigma_x$ for logarithmic and power functions).