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 (
    8338, 8339, 8724, 8346, 8341, 8462, 8334, 
    8335, 8355, 8725, 8342, 8340, 8360, 
    8064, 8473, 8332, 8267, 8318, 8336, 
    7056, 8337, 8243, 8257, 8381, 8315, 
    8265, 8313
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'ru' 
  AND (
    cscart_seo_names.company_id = 1 
    OR cscart_seo_names.company_id = 0
  )

Query time 0.00095

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "37.81"
    },
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "dispatch"
      ],
      "key": "PRIMARY",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code",
        "company_id"
      ],
      "key_length": "210",
      "rows_examined_per_scan": 54,
      "rows_produced_per_join": 54,
      "filtered": "100.00",
      "index_condition": "((`primapearl_r_new`.`cscart_seo_names`.`object_id` in (8338,8339,8724,8346,8341,8462,8334,8335,8355,8725,8342,8340,8360,8064,8473,8332,8267,8318,8336,7056,8337,8243,8257,8381,8315,8265,8313)) and (`primapearl_r_new`.`cscart_seo_names`.`type` = 'p') and (`primapearl_r_new`.`cscart_seo_names`.`dispatch` = '') and (`primapearl_r_new`.`cscart_seo_names`.`lang_code` = 'ru') and ((`primapearl_r_new`.`cscart_seo_names`.`company_id` = 1) or (`primapearl_r_new`.`cscart_seo_names`.`company_id` = 0)))",
      "cost_info": {
        "read_cost": "32.41",
        "eval_cost": "5.40",
        "prefix_cost": "37.81",
        "data_read_per_join": "91K"
      },
      "used_columns": [
        "name",
        "object_id",
        "company_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
7056 190-1-1058r 266/265
8064 390-1-306r 266/268
8243 390-1-715r 266/268
8257 390-1-744r 266/268
8265 390-1-752r 266/268
8267 390-1-755r 266/268
8313 390-1-808r 266/268
8315 390-1-810r 266/268
8318 390-1-814r 266/268
8332 390-1-829r 266/268
8334 390-1-831r 266/268
8335 390-1-832r 266/268
8336 390-1-833r 266/268
8337 390-1-834r 266/268
8338 390-1-835r 266/268
8339 390-1-836r 266/268
8340 390-1-837r 266/268
8341 390-1-841r 266/268
8342 390-1-842r 266/268
8346 390-1-851r 266/268
8355 390-1-861r 266/268
8360 390-1-867r 266/268
8381 390-1-902r 266/268
8462 pl001 266/268
8473 pl8033 266/268
8724 kole 266/278
8725 sergi-ru-2 266/267