SELECT 
  cscart_seo_names.object_id AS product_id, 
  cscart_seo_names.name AS seo_name, 
  cscart_seo_names.path AS seo_path 
FROM 
  cscart_seo_names 
WHERE 
  cscart_seo_names.object_id IN (
    583, 573, 1040, 1072, 1022, 1023, 1054, 
    1053, 1070, 815, 811, 820
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'ru'

Query time 0.00057

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "28.81"
    },
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "dispatch"
      ],
      "key": "PRIMARY",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code"
      ],
      "key_length": "206",
      "rows_examined_per_scan": 12,
      "rows_produced_per_join": 12,
      "filtered": "100.00",
      "index_condition": "((`cscart`.`cscart_seo_names`.`object_id` in (583,573,1040,1072,1022,1023,1054,1053,1070,815,811,820)) and (`cscart`.`cscart_seo_names`.`type` = 'p') and (`cscart`.`cscart_seo_names`.`dispatch` = '') and (`cscart`.`cscart_seo_names`.`lang_code` = 'ru'))",
      "cost_info": {
        "read_cost": "26.41",
        "eval_cost": "2.40",
        "prefix_cost": "28.81",
        "data_read_per_join": "20K"
      },
      "used_columns": [
        "name",
        "object_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
573 myagkoe-kreslo-transformser-tivoli-dub-shampan-maxx-100 403/300
583 myagkoe-kreslo-holli-velutto-04 403/300
811 pismennyy-stol-pravyy-kassiya 392/394/397
815 pismennyy-stol-kassiya 392/394/416
820 pismennyy-stol-s-podemnoy-kryshkoy-allegro-levyy 392/394/416
1022 obuvnica-gala 309/347
1023 obuvnica-sharli 309/347/361
1040 nalivnoy-pol-granit-l-60-20-kg 417/421
1053 peschano-cementnaya-smes-granit-s-150-25kg 417/430
1054 peskobeton-granit-m-300-25-kg 417/431
1070 peschano-cementnaya-smes-piramix-unimix-m-150-25-kg 417/430
1072 nalivnoy-pol-piramix-finishfloor-25-kg 417/421