Dominykas

See how it's done in products.json file:

We have the parent Variable product with  "attribute_name": "Gendre" . If your variable product belongs to more than one attribute, then add it. For example: "attribute_name2": "Size".

--------------------------------------------
  {
    "product_id": 200,
    "type": "variable",
    "name": "My product 2",
    "description": "My product description 2",
    "regular_price": 0,
    "manage_stock": 0,
    "stock": 0,
    "weight": 0,
    "attribute_name": "Gendre",
    "attribute_name2": "Size",
    "has_variations": 1
  }
--------------------------------------------

Secondly, what we have here is a child product variation:
Here we assign a product variation to a certain attribute and its value. "attribute_name": "Gendre" and "attribute_value": "Woman". Here, I will also add our second attribute "attribute_name2": "Size" and value  "attribute_value2": "Small",

{
    "type": "product_variation",
    "parent_product_id": 200,
    "description": "My product variation 1",
    "regular_price": 120,
    "manage_stock": 1,
    "stock": 5,
    "weight": 0,
    "attribute_name": "Gendre",
    "attribute_value": "Woman",
    "attribute_name2": "Size",
    "attribute_value2": "Small"
}

What you to do next is to go over the import script and process attribute_name2 and attribute_value2 too.

function get_attributes_from_json( $json ) - should include attribute_name2 and attribute_value2 too.

The same is function get_products_and_variations_from_json( $json, $added_attributes )  - your attribute_name2 and attribute_value2 should be there...