Заполните пропуски ниже. They have two children. What are ... names?

The correct answer is 'their'. The sentence should read: 'They have two children. What are their names?' The word 'their' is a possessive pronoun that indicates that the names belong to the children. 'Theirs' is a possessive pronoun used without a following noun and doesn't fit in the sentence, and 'our' indicates possession by the speaker or a group including the speaker which doesn't match the context. Therefore, the correct answer is 'their'.