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 (
    51422, 51424, 51429, 51430, 51423, 51431, 
    51425, 51426
  ) 
  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 0.00062

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "11.21"
    },
    "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": 16,
      "rows_produced_per_join": 16,
      "filtered": "100.00",
      "index_condition": "((`test_uchur_k`.`cscart_seo_names`.`object_id` in (51422,51424,51429,51430,51423,51431,51425,51426)) and (`test_uchur_k`.`cscart_seo_names`.`type` = 'p') and (`test_uchur_k`.`cscart_seo_names`.`dispatch` = '') and (`test_uchur_k`.`cscart_seo_names`.`lang_code` = 'ru') and ((`test_uchur_k`.`cscart_seo_names`.`company_id` = 1) or (`test_uchur_k`.`cscart_seo_names`.`company_id` = 0)))",
      "cost_info": {
        "read_cost": "9.61",
        "eval_cost": "1.60",
        "prefix_cost": "11.21",
        "data_read_per_join": "27K"
      },
      "used_columns": [
        "name",
        "object_id",
        "company_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}