What's the name of the rule of inference where we conclude $p$ implies $q$, given the premise $p$ and $q$? 
What's the name of the rule of inference where we conclude $p$ implies $q$, given the premise $p$ and $q$?

Premise: $p$ and $q$.
Conclusion: $p$ implies $q$ (or the converse).
What's the name of this rule of inference?

Going from $p$ and $q$ to $p \to q$ is not a very interesting inference, and it has no name.
A more interesting inference is going from $q$ alone to $p \to q$. And that one is sometimes called 'Conditionalization'
Indeed, the fact that you can get to $p \to q$ from $q$ alone is exactly why going to $p \to q$ on the basis of $q$ and $p$ is uninteresting, as the $p$ turns out to be completely unncessary in this inference.  You might as well ask the name for:
$q \to r$
$q$
$p$
$\therefore r$
