Export independently PDF with script

In addition to what my colleagues mentioned, three additional points:

1. It's more efficient first to check whether there are any pages with missing frames, and if there are, show them all and quit.

2. No need to bind the preset to a variable at every iteration of the loop: do it once (and check whether it exists).

3. You can access a labelled text frame directly, no need for a loop -- if you labelled them on the Layers panel.

4. To obtain the contents of a frame, address its parent story to avoid problems with overset text.

That's rather a lot, so I recast your script:

var myDocument = app.activeDocument;
// Use an array, much faster than a collection
var myPages = myDocument.pages.everyItem().getElements();
var myPage, myFile;
var missing = [];

//Check whether the preset is present

var myPDFExportPreset = app.pdfExportPresets.item("[PDF/X-3:2002]");
if (!myPDFExportPreset.isValid) {
  alert ("Preset not found");
  exit();
}

// Then check whether there are any pages without the frame

for (var i = 0; i < myPages.length; i++) {
  if (!myPages[i].textFrames.item("nombreDestinatario").isValid) {
    missing.push (myPages[i].name);
  }
}

// Any missing frames? Show them and quit

if (missing.length > 0) {
  alert("No se encontró la caja de texto 'nombreDestinatario' en las páginas " + missing.join(', '));
  exit();
}


for (var i = 0; i < myPages.length; i++) {
  myPage = myPages[i];
  // Use the parentStory to avoid problems with overset
  myFileName = myPage.textFrames.item("nombreDestinatario").parentStory.contents;
  // ~/Desktop/ is a shortcut for the current user's desktop
  myFile = File("~/Desktop/alumnos/" + myFileName + ".pdf");
  app.pdfExportPreferences.pageRange = myPage.name;
  myDocument.exportFile(ExportFormat.pdfType, myFile, false, myPDFExportPreset);
}