The Repetition of a vowel sound in nearby words is called-

• The Repetition of a vowel sound in nearby words (without the recurrence of consonant sounds which would make a rhyme) is called assonance.
• An example of Assonance:
Alone, alone, all, all alone;
Alone on a wide, wide sea'
Source: An ABC of English Literature, Dr M Mofizar Rahman.