The repeating of opening consonant sounds is nearly always referred to as an example of alliteration. Some scholars prefer to conceive of vowel sounds as a form of assonance rather than a part of the definition. Assonance is more of a literal term which indicates towards the repeating of vowel sounds between the words, whether at the initial, midway, or ending section.
Consonance is a similar concept that refers to the repetition of consonant sounds in consecutive words. Because it solely applies to sounds that are repeated in the starting of words, alliteration is considered a subset of consonance.
These dramatic strategies may be employed solo, or in combined format to make poem, writings, or the speech discourse more interesting.