Final answer:
The sentence 'My two dogs are named Hannah and Brindle' is a simple sentence because it contains only one main clause with a single complete idea.
Step-by-step explanation:
The sentence in question, "My two dogs are named Hannah and Brindle," is a simple sentence. A simple sentence consists of a single main clause, which contains a subject and a predicate, and can stand alone as a sentence. The sentence provided does not have multiple main clauses or any subordinate clauses, thus it does not qualify as a compound, complex, or compound-complex sentence.