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 (
    10390, 10389, 10388, 10387, 10386, 10384, 
    10383, 10382, 12679, 12678, 12677, 
    12676, 12675, 12674, 12673, 15779, 
    12672, 12671, 12994, 12993, 12992, 
    12991, 12990, 12989, 12988, 12987, 
    12986, 12985, 10343, 10345, 10346, 
    10347
  ) 
  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 0.00091

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": 64,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (10390,10389,10388,10387,10386,10384,10383,10382,12679,12678,12677,12676,12675,12674,12673,15779,12672,12671,12994,12993,12992,12991,12990,12989,12988,12987,12986,12985,10343,10345,10346,10347) 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)"
    }
  }
}