После разрыва слова выровняйте следующую строку по левому краю, а не по центру

.justify {
  text-align: justify;
  text-justify: inter-word;
}

.paragraph {
  text-align: center;
  max-width: 220px;
  word-wrap: break-word;
  word-break: break-all;
  text-align-last: left;
  border: 1px solid red;
}

<div class='justify'>
  <p class = "paragraph">Hello, my name is Taylor and welcome to my personal website!</p>
</div>

.justify {
  text-align: justify;
  text-justify: inter-word;
}

.paragraph {
  text-align: left;
  max-width: 220px;
  word-wrap: break-word;
  word-break: break-all;
}

<div class='justify'>
  <p class = "paragraph">Hello, my name is Taylor and welcome to my personal website!</p>
</div>