Insert a variable on many pages in Adobe InDesign to fill in when printing PDF

You can do it with scripting. I've tried an tested this script in InDesign CS5 on a Mac, What you need to do is

• Select which text box you want the students' name to go in
• Then under the 'layers' panel, expand the layer it is in, and change the name of the text box by slow double clicking it, and enter "NAME"
• Copy and paste the script below in notepad or textedit
• Edit the first line to var students = ["First Student", "Second Student"]; etc. (Hopefully this doesn't take longer than if you were not to use the script)
• Save as MakePdfForEachStudent.jsx and save it in /Applications/Adobe InDesign CS5.5/Scripts/Scripts Panel/Samples/Javascript if you're on Mac (I can't remember where it is on Windows)
• Go to Window > Utilities > Scripts and select MakePdfForEachStudent.jsx
• Follow the process

Hope this helps/works. I may improve this answer later.

// An InDesign CS5 javascript macro for exporting PDFs with different student names.

var students = ["Peter", "Lois", "Meg", "Chris", "Brian"];
var studentsNameTextLayer = "NAME";

// DON'T EDIT BELOW THIS LINE

// Display a "choose folder" dialog box.
if (app.documents.length != 0) {
    var myFolder = Folder.selectDialog ("Choose a Folder");
    if (myFolder != null) {
        myExportPages(myFolder);
    }
} else {
    alert("Please open a document and try again.");
}

function myExportPages(myFolder)
{
    var studentName, myFilePath, myFile;

    var myDocument      = app.activeDocument;
    var myDocumentName  = myDocument.name;
    var theDialog       = app.dialogs.add();
    var myPageName      = myDocument.pages.item(0).name;
    var textBoxName     = myDocument.pages.item(0).textFrames.item(whichTextBox);

    with (theDialog.dialogColumns.add().dialogRows.add()) {

        staticTexts.add({
            staticLabel: "Base name:"
        });

        var myBaseNameField = textEditboxes.add({
            editContents : myDocumentName, 
            minWidth : 160
        });
    }

    var myResult = myDialog.show({
        name : "ExportPages"
    });

    if (myResult == true) {
        var myBaseName = myBaseNameField.editContents;

        // Remove the dialog box from memory.
        theDialog.destroy();

        for (var loopCounter = 0; loopCounter < students.length; loopCounter++) {
            studentName = students[loopCounter];

            studentsNameTextLayer.contents = studentName;

            app.pdfExportPreferences.pageRange = myPageName;

            var matchColon  = new RegExp(":","gi");

            myPageName  = myPageName.replace(matchColon, "_");
            myFilePath  = myFolder + "/" + myBaseName + "_" + myPageName + "_" + studentName + ".pdf";
            myFile      = new File(myFilePath);

            myDocument.exportFile(ExportFormat.pdfType, myFile, false);
        }

    } else {
        theDialog.destroy();
    }
}