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 (
    12588, 12605, 12606, 12637, 12612, 12613, 
    12641, 12554, 12552, 12642, 12648, 
    12611, 12596, 12607, 12608, 12610, 
    12643, 12649, 12609, 12644, 12650, 
    12652, 12653, 12654, 12646, 12655, 
    12656, 12645, 12651, 12597, 12615, 
    12603
  ) 
  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 0.00096

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 (12588,12605,12606,12637,12612,12613,12641,12554,12552,12642,12648,12611,12596,12607,12608,12610,12643,12649,12609,12644,12650,12652,12653,12654,12646,12655,12656,12645,12651,12597,12615,12603) 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)"
    }
  }
}