What is the function of the complement shown in parentheses in this sentence "We named our (Australian shepherd) Allie" ?
"Australian Shepherd" is the Direct Object in the sentence.
Subject of sentence: We
Verb : named
Direct Object : shepherd
Modifiers of Direct Object: our Australian
Object Complement: Allie (Proper Noun)
[I would consider just "shepherd" to be the D.O., because there are different kinds of shepherd dogs. What kind of shepherd dog? A German shepherd; an Australian shepherd.]
The Original Answer is correct, but perhaps somewhat terse:
subject + Factitive Verb + Object + Objective Complement/Noun Complement/Factitive Object
We named OUR AUSTRALIAN SHEPHERD Allie.
OUR AUSTRALIAN SHEPHERD == Object (not complement)