Elasticsearch query string query with not equal to?

You need to use the NOT operator, like this:

!(name:"Fred")

or

NOT (name:"Fred")

You can also use a combination of must and must_not. Like pull docs where name is Ajit and status is not queued.

{
    "query": {
        "bool": {
            "must": [
                {
                    "match": {
                        "name": "Ajit"
                    }
                }
            ],
            "must_not": [
                {
                    "match": {
                        "status": "queued"
                    }
                }
            ]
        }
    }
}

You should use bool query with must_not statement

{
  "query": {
    "bool" : {
      "must_not" : {
        "term" : {
          "name" : "Fred"
        }
      }
    }
  }
}