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The "HAVE SOMETHING DONE" structure has no other name, but if you learn its name, you will know how to use it: we need to say or write the verb HAVE (in any tense, depending on the context), followed by a direct object (a pronoun or a noun phrase) and a verb in the past participle.
When I say that I am going to have something done, I mean that I am going to pay a professional to do something for me. For example, if I need my blood analysed, I can say: "I need to HAVE SOME BLOOD TAKEN OUT for an analysis."
So, in every case you will see the verb HAVE (in this example, in infinitive because it appears after the auxiliary NEED TO), followed by the Od of the sentence (SOME BLOOD) and a verb in the past participle (TAKEN OUT); it is a similar structure to the passive voice, that's why they are usually studied together.