I know that (¬p → q) ≡ (p v q) from comparing the truth tables. But is there a law that states this? Something like the laws of propositional logic: idempotent, associative, commutative, distributive, etc.?
The rule is called material implication in classical logic. Here's Wikipedia's description:
In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not-P or Q and that either form can replace the other in logical proofs.
In more detail one has (¬p → q) ≡ (¬¬p v q) by material implication. By double negation elimination one can change ¬¬p to p.
This is also presented in Wikipedia's list of logical equivalences involving conditional statements.
Wikipedia contributors. (2019, July 6). Material implication (rule of inference). In Wikipedia, The Free Encyclopedia. Retrieved 00:04, August 31, 2019, from https://en.wikipedia.org/w/index.php?title=Material_implication_(rule_of_inference)&oldid=905048316