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 (
    388, 426, 409, 404, 1936, 387, 386, 416, 
    441, 322
  ) 
  AND cscart_seo_names.type = "p" 
  AND cscart_seo_names.dispatch = "" 
  AND cscart_seo_names.lang_code = 'en' 
  AND (
    cscart_seo_names.company_id = 1 
    OR cscart_seo_names.company_id = 0
  )

Query time 0.00076

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "48.01"
    },
    "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": 20,
      "rows_produced_per_join": 20,
      "filtered": "100.00",
      "index_condition": "((`eshopuga_upgr_4122`.`cscart_seo_names`.`object_id` in (388,426,409,404,1936,387,386,416,441,322)) and (`eshopuga_upgr_4122`.`cscart_seo_names`.`type` = 'p') and (`eshopuga_upgr_4122`.`cscart_seo_names`.`dispatch` = '') and (`eshopuga_upgr_4122`.`cscart_seo_names`.`lang_code` = 'en') and ((`eshopuga_upgr_4122`.`cscart_seo_names`.`company_id` = 1) or (`eshopuga_upgr_4122`.`cscart_seo_names`.`company_id` = 0)))",
      "cost_info": {
        "read_cost": "44.01",
        "eval_cost": "4.00",
        "prefix_cost": "48.01",
        "data_read_per_join": "33K"
      },
      "used_columns": [
        "name",
        "object_id",
        "company_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
322 full-of-wishes 328/335/349
386 white-rose-brightness 328/336/337
387 white-paradise 328/336/337
388 splendid-awesomeness 328/336/337
404 sweet-sunshine 328/336/337
409 surprise-me 328/336/337
416 wrap-me-in-red 328/336/337
426 lots-of-energy 328/336/337
441 yellow-passion 328/336/337
1936 aplus-love-basket 329/361