I always asked myself what was the right method name for a simple linear regression using *running* parameters.

I mean that instead of using constant mean $\bar{y}$ or $\bar{x}$ for the estimation of $ \alpha$ we use a simple moving average of $x$ and $y$ as well as a running standard deviation and a running correlation coefficient. 

I've heard of least square moving average as well as local regression/running line but I'm not sure what is the correct formulation of such a method.