Is there an accepted term (an adjective or prefix) like strict, trichotomous, strong or definite sign to indicate the three-valued sign whose values are $+$, $-$, and $0$?
Are there words reserved for this use in mathematical languages besides English?
An example is functions or differential equation solutions that do not change "sgn". So to speak.
Edit. The phrase should retain the word "sign" and add to it an adjective, prefix or (less likely) a suffix. So, "super-sign (it)" is hypothetically a candidate, but not necessarily signito, sssignnnn, signulus, signifier, signiance, signplusplus.
The signum function meets your criteria.