The solution is short, yet may look a bit tricky, so here I provide it with extensive comments:

```js
let sortedRows = Array.from(table.tBodies[0].rows) // 1
  .sort((rowA, rowB) => rowA.cells[0].innerHTML.localeCompare(rowB.cells[0].innerHTML));

table.tBodies[0].append(...sortedRows); // (3)
```

The step-by-step algorthm:

1. Get all `<tr>`, from `<tbody>`.
2. Then sort them comparing by the content of the first `<td>` (the name field).
3. Now insert nodes in the right order by `.append(...sortedRows)`.

We don't have to remove row elements, just "re-insert", they leave the old place automatically.

P.S. In our case, there's an explicit `<tbody>` in the table, but even if HTML table doesn't have `<tbody>`, the DOM structure always has it.