Does this behavior have a formal name, and if so, what is it?
In many programming languages above statement always returns true, due to that the 3 conditions using negation are checked independently of each other.


It returns true not just due to "that the 3 conditions using negation are checked independently of each other", but because the expression (v != "x" || v != "y" || v != "z") is always necessarily true. In logic such expressions are called tautology, i.e. a formula that is true in every possible interpretation (Wikipedia). 

But "this behavior or situation" does not have a special name in programming and is usually considered as a programming error.