The question is pretty straightforward.
The variance of a random variable $X$ with mean $\mu$ is defined as $\mathrm E[(X-\mu)^2]$ and is notated $\operatorname{Var}(X)$ or $\sigma^2$.
Another measure of central tendency could be defined: $\mathrm E[X-\mu]$. I’d simply like to know if this has a name. If not, that’s okay.
$\newcommand{\E}{\mathrm{E}} \E[X-\mu]=\E[X]-\E[\mu]=\E[X]-\mu=\mu-\mu=0$. I have used the fact that expectation is linear and expectation of a constant is the constant itself.