Relative to $(p \implies q)$, the expression $(\lnot p \implies \lnot q)$ is the converse, since the second conditional is equivalent to $(q \implies p)$ (by contraposition).
Does the relation between $(\lnot p \implies q)$ and $(p \implies q)$ have a name? What is the first expression relative to the second?
Since $(\lnot p \implies q)$ is equivalent to $(p \lor q)$, the relationship between $(\lnot p \implies q)$ and $(p \implies q)$ is the same as the relationship between $(p \lor q)$ and $(p \implies q)$. But since these are two different connectives there is no need to have a name for the relationship between them.