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 (
    1540, 2082, 2404, 1516, 2405, 1545, 352, 
    2092, 2400, 366, 1517, 356
  ) 
  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 0.00048

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": 24,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (1540,2082,2404,1516,2405,1545,352,2092,2400,366,1517,356) 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
352 160x230-fresco-833-671470 302/303/321
356 160x230-mirror-805-c-577670 302/303/321
366 belgiyskiy-kover-160h230-bauhaus-col.474640 302/303/321
1516 80x125-chic-512-s-497161 302/303/430
1517 80x125-apatite-342-s-497140 302/303/430
1540 shabby-998c477440 302/303/306
1545 florense-809c677475 302/303/306
2082 belgiyskiy-kover-200x300-basalt-773-s-677230 302/303/306
2092 belgiyskiy-kover-160x230-djotto 302/303/306
2400 tureckiy-kover-penthouse-shr-papatya-160x230 302/303/304
2404 tureckiy-kover-wave-160x230 302/303/304
2405 tureckiy-kover-zebra-bone-bone-160x230 302/303/304