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 (
    10504, 10503, 10502, 10501, 10500, 10499, 
    10498, 10497, 12592, 12591, 12590, 
    12588, 13091, 12623, 12587, 12585, 
    12595, 12593, 12620, 12619
  ) 
  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 0.00064

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": ["PRIMARY", "dispatch"],
      "key": "PRIMARY",
      "key_length": "210",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code",
        "company_id"
      ],
      "rows": 40,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (10504,10503,10502,10501,10500,10499,10498,10497,12592,12591,12590,12588,13091,12623,12587,12585,12595,12593,12620,12619) 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)"
    }
  }
}

Result

product_id seo_name seo_path
10497 garmoniya-rogozhka-col-05 265/280/439/455
10498 garmoniya-rogozhka-col-04 265/280/439/455
10499 garmoniya-rogozhka-col-03 265/280/439/455
10500 garmoniya-rogozhka-col-02 265/280/439/455
10501 garmoniya-rogozhka-col-01 265/280/439/455
10502 garmoniya-miks-col-07 265/280/439/455
10503 garmoniya-miks-col-06 265/280/439/455
10504 garmoniya-miks-col-05 265/280/439/455
12585 tureckiy-kover-donna-satin-silver-200h300 265/266/1688
12587 tureckiy-kover-donna-antik-gold-200h300 265/266/1688
12588 tureckiy-kover-good-night-blue-152h200 265/266/267
12590 belgiyskiy-kover-prisma-200x300 265/266/277
12591 belgiyskiy-kover-porto-200x300 265/266/278
12592 belgiyskiy-kover-djotto-200x290 265/266/278
12593 tureckiy-kover-donna-antique-copper-300x400 265/266/1688
12595 tureckiy-kover-donna-antik-gold-160x230 265/266/1688
12619 tureckiy-kover-donna-satin-silver-160x230 265/266/1688
12620 tureckiy-kover-donna-pearl-160x230 265/266/267
12623 tureckiy-kover-donna-pearl-200h300 265/266/270
13091 tureckiy-kover-balloons-grey-152h200 265/266/267