Length normalisation in elasticsearch cross_field multi_match

Question

I am currently implementing a search for people names in a database. It's a structured document that has 3 fields: firstName, middleName, lastName. I started using the cross_fields multi_match query and it works fine unless one corner case. This is the query that I run:

"multi_match": {
  "fields": [
    "name.firstName^2",
    "name.middleName",
    "name.lastName^3"
  ],
  "query": "John Smith",
  "operator": "AND",
  "type": "cross_fields"
}

I would like the object to be treated as one single long field, but boosted in the order lastName, firstName. The problem is that the following documents get the same score:

{
    "firstName": "John",
    "lastName": "Smith"
}

and

{   
    "firstName": "John",
    "middleName": "Adams",
    "lastName": "Smith"
}

while if you consider length of a "concatenated" field, the first one is 2/2 match and the second is 2/3 match, so 2/2 should be scored higher.

In other words, I would like to perform length normalization in all fields in the multi_match query, not per-field normalization.

Could you advise me how to achieve this?

Thanks!