But "completeness" already has a (different) definition, like when we say the reals are complete but the rationals are not edit: to match with existing termino

But "completeness" already has a (different) definition, like when we say the reals are complete but the rationals are not edit: to match with existing terminology you might call the reals the "completes" and the complex numbers the "algebraically-closeds" but... meh.