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 (
    10696, 10695, 10693, 10692, 15958, 15957, 
    15956, 12600, 12602, 12604, 12606, 
    12608, 12603, 12615, 12597, 12609, 
    12610, 12607, 12596, 12611, 12613, 
    12612, 12605, 12601, 12616, 12599, 
    10666, 10664, 10663, 10661, 10659, 
    10658
  ) 
  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 0.00095

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 (10696,10695,10693,10692,15958,15957,15956,12600,12602,12604,12606,12608,12603,12615,12597,12609,12610,12607,12596,12611,12613,12612,12605,12601,12616,12599,10666,10664,10663,10661,10659,10658) 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)"
    }
  }
}