literary device where multiple words in a row begin with the same consonant sound

This is called an Alliteration

Explanation:

In literature, alliteration is the conspicuous repetition of identical initial consonant sounds in successive or closely associated syllables within a group of words, even those spelled differently. As a method of linking words for effect, alliteration is also called head rhyme or initial rhyme.

A classic example is:“She sells seashells by the sea-shore.”

the characters in string all have major secrets that they strive to avoid revealing throughout the play.