Variables

Simple enough to do with a custom JavaScript.

Name your .ai file’s text frames “LABEL 1”, “LABEL 2”, “LABEL 3”, etc in the Layers palette, as shown in the screenshot, and re-save it. Save the script as “update template labels.jsx”.

With the .ai template open in Illustrator, choose File > Scripts > Other Script... and select the “update template labels.jsx” script. It will prompt you to select your .csv data file (its headings must match the 3 column headings shown in your screenshots), and will update the existing text frames with the new data.

// update template labels.jsx

// Read lines from a comma-separated text file and insert each line's values into a named text frame in the AI document.

// This code is released into the Public Domain.


(function() {


function parseCSVLine(data, headings) {
  // Parses one line of CSV data, returning it and the remaining data
  // data : string -- the CSV data
  // headings : [string] | undefined -- undefined when reading first (headings) line
  // Result: {fields: {string} | [string], data: string} --the line's fields plus any remaining lines of CSV data
  //
  // Notes: On return, fields is an object if headings array is given (headings are used as object keys), or an array of fields if no headings are provided. The number of headings must match the number of CSV fields, otherwise an error is thrown.
  var col = 0, eol = false; fields = headings ? {} : [];
  while (!eol) { // find next comma or double quote, or end of line
    var value = '', done = false, m = data.match(/[",]|[\r\n]+/);
    switch ((m || '')[0]) {
    case ',':
      value = data.slice(0, m.index);
      data = data.slice(m.index + 1); // step over text + comma
      break;
      
    case '"': // quoted field
      data = data.slice(1); // discard opening quote
      while (!done && data) {
        m = data.match(/"/);
        // note: quoted values can include line breaks so all we can do is read to next double-quote character
        if (!m) { throw new Error("Missing double-quote at end of CSV column " + col + "."); }
        var index = m.index;
        value += data.slice(0, index);
        if (data[index + 1] === '"') { // is the double quote followed by a second double quote (escape sequence)?
          value += '"'; // replace the 2 double quotes with 1
          index++;
        } else { // it's a single double-quote, which ends the quoted value
          done = true;
        }
        data = data.slice(index + 1); // step over quote(s)
      }
      data = data.slice(1); // step over comma
      break;
    
    default: // found end of line/end of file; last value is anything up to it
      if (m) {
        value = data.slice(0, m.index);
        data = data.slice(m.index + m[0].length); // step over text and comma
      } else {
        value = data;
        data = '';
      }
      eol = true;
    }
    if (headings) {
      var heading = headings[col];
      if (heading === undefined) { 
        throw new Error("Mismatched CSV columns: expected " + headings.length + " columns but found this value in column " + (col + 1) + ": '" + value + "'");
      }
      fields[heading] = value;
    } else {
      fields.push(value);
    }
    col++;
    if (col > 1000) { throw new Error("Too many CSV columns (this is probably a bug)."); }
  }
  if (headings && col !== headings.length) {
    throw new Error("Mismatched CSV columns (this is probably a bug).");
  }
  return {fields: fields, data: data};
}


function readFile(f) {
	f.encoding = 'utf-8';
  if (!f.open('r')) { throw new Error("Can't open file: " + f.fullName); }
  var s;
  try {
    s = f.read();
  } catch (e) {
    f.close();
    throw e;
  }
  f.close();
  return s;
}


// main

// prompt the user to select the CSV file manually each time:

var f = File.openDialog('Please choose the .CSV file:');

// OR, if the file is in a fixed location, replace the above line with this:

// var f = File('~/PATH/TO/INVENTORY.csv');

// (edit the path to the CSV file's actual location, e.g. '~/Documents/inventory.csv')

if (!f) { return; }

var data = readFile(f);

var headings = ['COLOR', 'QTY', 'ORDERNO']; // these MUST match the spreadsheet headings

data = parseCSVLine(data).data; // step over the headings line

var doc = app.activeDocument;

// read each line of the CSV and insert into text frame named 'LABEL 1', 'LABEL 2', 'LABEL 3', etc.
var i = 1;
while (data) {
  try {
	var result = parseCSVLine(data, headings);
	data = result.data;
	fields = result.fields;
	doc.textFrames.getByName('LABEL '+ i).contents = fields.COLOR + '\n' + fields.QTY + '\n' + fields.ORDERNO;
	i++;
	} catch (e) {
	  alert("Error processing CSV line " + (i + 1) + ": " + e);
	  return;
	}
}
alert("Updated " + (i - 1) + " labels."); // delete this line if you don't want the confirmation message

}());

I already had the functions written so it was just a matter of adding the loop and testing it; 15 minutes work (plus the time to write this post). If this solves your problem a $30 donation to a homeless charity of your choice is appreciated.