An earlier reference than Garner–Hirschowitz's paper is Tholen's MacNeille completion of concrete categories with local properties (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).

Assuming uniqueness of the automorphism, an earlier reference than Garner–Hirschowitz's paper is Tholen's MacNeille completion of concrete categories with local properties (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.