Append Prefix to Field

I have several documents such as:

    {
    "_id" : "60d3fcb6077b0a41e090ecc9",
    "vendor" : "Best",
    "test_name" : "Number Sequence",
    "discipline" : "early math"
},
{
    "_id" : "60d3fcb6077b0a41e090edd7",
    "vendor" : "Best",
    "test_name" : "Value Places",
    "discipline" : "early math"
}

I would like to append EM: to the test_name field, regardless of what is already in that field as long as it matches the vendor and discipline fields.

Here is what I have tried so far:

db.getCollection("assessments_1234").aggregate(
    [
        {
            "$match" : {
                "vendor" : "Best",
                "discipline" : "early math"
            }
        }, 
        {
            "$set" : {
                "test_name" : {
                    "$cond" : {
                        "if" : {
                            "$regexMatch" : {
                                "input" : "$test_name",
                                "regex" : /.* /
                            }
                        },
                        "then" : {
                            "$replaceOne" : {
                                "input" : "$test_name",
                                "find" : "",
                                "replacement" : "EM: "+"$test_name"
                            }
                        },
                        "else" : "$test_name"
                    }
                }
            }
        }
    ], 
    {
        "allowDiskUse" : false
    }
).forEach(function(record) {
    print(record.test_name)
   db.assessments_1234.replaceOne({_id: record._id}, record)
})

Actually, you can work the update with the aggregation pipeline, which directly perform the update in the MongoDB server, without the need to fetch the record to the backend and update them one by one back to the MongoDB server.

1. For the string concatenation, you should use $concat operator.
2. As you want string concatenation, you should not need the $replaceOne operator.

db.getCollection("assessments_1234").update({
  "vendor": "Best",
  "discipline": "early math"
},
[
  {
    "$set": {
      "test_name": {
        "$cond": {
          "if": {
            "$regexMatch": {
              "input": "$test_name",
              "regex": ".*"
            }
          },
          "then": {
            $concat: [
              "EM: ",
              "$test_name"
            ]
          },
          "else": "$test_name"
        }
      }
    }
  }
],
{
  multi: true
})

Demo @ Mongo Playground

As you mentioned that you want to update the field_name without concern its value, perhaps you can simplify the query without the need of $cond operator.

db.getCollection("assessments_1234").update({
  "vendor": "Best",
  "discipline": "early math"
},
[
  {
    "$set": {
      "test_name": {
        $concat: [
          "EM: ",
          "$test_name"
        ]
      }
    }
  }
],
{
  multi: true
})

Demo (without $cond) @ Mongo Playground