The relation that you have results from the Wiener-Khinchin theorem (WK). The WK theorem primarily relates the autocorrelation of the input and its power spectral density (PSD) as a Fourier transform pair. I have not heard it referred to by any particular name other than explicitly saying "From the WK theorem, we have blah..." From the article cited:
A corollary [of the WK theorem] is that the Fourier transform of the autocorrelation function of the output of an LTI system is equal to the product of the Fourier transform of the autocorrelation function of the input of the system times the squared magnitude of the Fourier transform of the system impulse response.
While it was written and proven for signals (or functions) that are square integrable, and hence have a Fourier transform, it is commonly used to study WSS random processes (which do not have a Fourier transform) by relating the autocorrelation via expectations rather than integrals.