Alliteration is the repetition of the beginning sounds of words, like when Juliet says that parting was "such sweet sorrow" in Act 2 of Romeo and Juliet. Authors often choose to use alliteration to make certain phrases memorable or poetic, or simply to add emphasis. (Other times, random chance causes authors to simply use the same sounds to begin words close together in a phrase--although you can still call these instances "alliteration," you might better understand them as coincidences of language, like when reporters mention "legal liability" or "past practices.")
If you take a look at Chapter 1 of Anthem, you'll notice quite a few alliterative phrases, such as "memory of men," "thin threads," "Street Sweepers," "your body has grown beyond the bodies of your brothers," "big bell," and more.
Are these examples evidence of purposeful alliteration? Probably. I say this because these particular alliterative phrases help establish the serious, dramatic, foreboding tone of the chapter. Clearly the narrator is in distress throughout Chapter 1, struggling to express his fear and reflecting on the extremely rigid existence he's lived through so far. This narrator's tone of voice, sentence structure, and poetic phrases all combine to convey that fear and distress.