In the sentence
They named him John.
what sort of complement is "John"? The direct object is "him".
How does this relate to a sentence like
They made him do it.
John is an object complement here.
http://grammar.ccc.commnet.edu/grammar/objects.htm
In the sentence "They named him John," the word "John" is a predicate nominative complement. A predicate nominative is a noun or pronoun that follows a linking verb (in this case, "named") and renames or identifies the subject (in this case, "him"). So, "John" is the complement that identifies or renames the subject "him."
Now, let's relate this to the sentence "They made him do it." In this sentence, "him" functions as the direct object of the verb "made," similar to how "him" serves as the direct object in the sentence "They named him John."
However, unlike in the previous sentence with "named," there is no complement in the sentence "They made him do it." The verb "made" does not require a complement to complete its meaning. Instead, "do it" acts as a direct object complement, indicating what action "him" is being made to perform. So, in the sentence "They made him do it," there is a direct object ("him") and a direct object complement ("do it"), but no predicate nominative complement like in the sentence "They named him John."