Modification points:

• In your script, file is FileIterator.
• In your if statement, file.next() is used 2 times. In this case, 1st file.next() is different from 2nd file.next(). If the file of the filename name.csv are existing only one file, when 2nd file.next() is run, an error occurs. I thought that This might be the reason of your issue.
• When you want to move the processed file to the trash box, it is required to use setTrashed for the 1st file.next().

When above points are reflected to your script, it becomes as follows.

Modified script:

function importCSV () {
  const folder = DriveApp.getFolderById("xyz");
  const file = folder.getFilesByName("name.csv");
  if (file.hasNext()) {
    const f = file.next(); // Added
    const csvString = f.getBlob().getDataAsString(); // Modified
    const csvData = Utilities.parseCsv(csvString);
    const lastRow = csvSheet.getLastRow();
    csvSheet.getRange(lastRow+1,1,csvData.length,csvData[0].length).setValues(csvData);
    f.setTrashed(true); // Modified
  }
}

Reference:

• Class FileIterator