What is the common terminology to refer to the nth ancestor of a tree root?
Commonly used phrases include,


"vertex at height $h$",
"vertex at depth $d$",
"vertex at distance $d$ from the root".


"Subtree $n$" doesn't make any sense, except as the $n$th element in some enumeration of subtrees.

By the way, I'd avoid using $n$ for anything other than the number of vertices in the graph.  That bit of notation is so standard in graph theory that it's confusing for the reader to have $n$&nbsp;mean anything else.