To summarize here all the answers that people gave in comments:
There seems not to be a standard notation/terminology for $\bar{A}\setminus A$ in the literature.
Points in $\bar{A}\setminus A$ can be referred to as "limit/closure points not in $A$" or "external limit/closure points".
$\bar{A}\setminus A$ is different in general than the boundary/frontier of $A$ which is defined as $\bar{A}\setminus \mathrm{int}(A)$, where $\mathrm{int}(A)$ is the interior of $A$.
