It is usually called a gauge symmetry but it is kind of a misnomer and should better be called a gauge redundancy. It is artifical and only due to the mathematical formalism we are using. As an analogy, probably not a really good one, is that you could decide to describe temperatures with a complex number and just say temperature is invariant under translation along the imaginary axis. Sure, the symmetry is in your mathematics but it doesn't really tell you anything new or interesting. Besides of course that the imaginary part is actually redundant and you better described temperature with a real number instead.