How do adjust for the confounder of a confounder? we call the confounder of a confounder for treatment effect estimation? How do we adjust for the confounder of a confounder in order to compute unbiased estimates of the treatment effect of $A$ on $D$? See the causal graph (DAG) below:

What do we call the confounder $C$ (of a confounder $B$) - does we give such variables/confounders any special name?

Thank you for including the DAG!
The answer here is pretty straight-forward: you simply condition on both $C$ and $B.$ Neither $C$ nor $B$ is part of a collider, so you're not opening up new paths by doing so, and this conditioning closes all backdoor paths from $A$ to $D,$ enabling you to get the unbiased effect of $A$ on $D.$
I'm not aware of any special name for the $C$ relative to $B$ except "parent". I'm also not sure I would call $C$ a "confounder of a confounder". A confounder is a variable that sets up a backdoor path from the cause in which you're interested to the effect in which you're interested. But you're not interested in $B$ as a cause of anything, so it strikes me as moot in this situation. I would just call $C$ the parent of $B$ and leave it at that.
