Assuming uniqueness of the automorphism, an earlier reference than Garner–Hirschowitz's paper is Tholen's [MacNeille completion of concrete categories with local properties](https://core.ac.uk/download/pdf/293149837.pdf) (1979), in which these objects are called *quasi-initial* (Definition 1.1), defined as those objects that are weakly initial and *prequasi-initial* (which is exactly the automorphism condition you describe).

Another earlier reference is Huq's *Semilimits in Categories* (1991), where these (or their duals) are called *semiterminal objects*, again assuming uniqueness of the automorphism.