React Hook Form - custom MUI table component with checkbox

I'm trying to create a custom MUI table that works with react-hook-form. The table rows have a checkbox to indicate whether an item is selected or not. My issue is I am able to "send" the data to the rows in order to correctly display the selected rows. However, I don't see a way to "retrieve" the data in the scenario that it changes.

My Table Body:

export default function HobbyList({ name, hobbies }: Props) {
  const { control } = useFormContext();
  const [selected, setSelected] = useState<Array<Hobby>>(hobbies);

  return (
    <Card>
      <TableContainer>
        <Table>
          <Controller
            name={name}
            control={control}
            render={({ field }) => {
              console.log(selected);
              console.log(field);
              return (
                <TableBody>
                  {apiHobbies.map((row, index) => {
                    console.log(row);
                    const selectedIds = selected.map((selected) => selected.id);
                    return (
                      <FieldRow
                        key={row.id}
                        row={row}
                        selected={selectedIds.includes(row.id)}
                      ></FieldRow>
                    );
                  })}
                </TableBody>
              );
            }}
          />
        </Table>
      </TableContainer>
    </Card>
  );
}

My Table Row:

export default function FieldRow({ row, selected }: Props) {
  const { name } = row;

  return (
    <TableRow hover selected={selected}>
      <TableCell padding="checkbox">
        <Checkbox checked={selected} />
      </TableCell>

      <TableCell sx={{ display: "flex", alignItems: "center" }}>
        {name}
      </TableCell>
    </TableRow>
  );
}

Am I incorrect in creating a controller for the component? Should it instead be on the component?

If that's the case then how can I use the names to properly track the components?

I have created an example Sandbox below