Nope, it is not a Greek letter, notably it is not a lowercase delta. It is just some random made up symbol that looks like a letter D. Which is of course derived from delta, which is why it is all so damn confusing.

I think the symbol is usually just read as "D" as in "d f d x" for $∂x∂F(x,y,z) $.

This notation is not so common in basic mathematics, but it is so incredibly convenient, especially with Einstein notation as shown at Section "Einstein notation for partial derivatives":

$∂_{0}F(x,y,z)=∂x∂F(x,y,z) ∂_{1}F(x,y,z)=∂y∂F(x,y,z) ∂_{2}F(x,y,z)=∂x∂F(x,y,z) $

This notation is similar to partial label partial derivative notation, but it uses indices instead of labels such as $x$, $y$, etc.