"The Unknown Citizen" features some some key instances of alliteration. The first occurs across lines 7 and 8:
He worked in a factory and never got fired,
But satisfied his employers, Fudge Motors Inc.
This section describes the unknown citizen's working life. The repeated /f/ links "factory," "fired," and "Fudge" together, the forceful sound suggesting the power and might of the state-approved corporation.
In lines 14, 16, and 17, alliteration is used to give the poem a particular rhythmic sound. The placement of "Press" and "paper," "Policies" and "prove," and "Health-card" and "hospital" are all quite uniform—the start of the line and roughly halfway through. The prominence of the alliterating sound thus becomes a kind of regular, bureaucratic process—like stamps being pressed onto official documents.
Next up is the phrase "Modern Man" in line 20. The alliteration here makes it sound like an advertising slogan, or some kind of ideologically-inspired concept thought up by the state. This reflects the poem's broader ideas about freedom and conformity in the modern world; society sells people an image of what a good life looks like, and people are compelled to recreate this image, thinking it will bring them happiness.
Another striking example of alliteration comes in line 24, in which the speaker discusses how the unknown citizen always held the officially-endorsed opinions:
When there was peace, he was for peace: when there was war, he went.
The idea here is to create a kind of echo—representing the way the dead man would always repeat what he was meant to. So when the State said "peace," he said "peace" too.