"The boy" is the syntactic object of "saw" but only the understood subject of "take". Syntactically, like most non-finite clauses, the infinitival clause "take the frog to a rock" is subjectless, though we understand it as having a subject, in this case "the boy".
Constructions like this where there are two or more adjacent verbs (sometimes separated by an intervening noun phrase) are called 'catenative'. The term 'catenative' comes from the Latin word for "chain", which is appropriate here since there is a chain of verbs.
In your example, the noun phrase "the boy" is called a 'raised' object, since the verb it relates to syntactically is higher in the constituent structure than the one it relates to semantically.