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 (
    10708, 10709, 10710, 10711, 10712, 10301, 
    10302, 10303, 10304, 9945, 10601, 9727, 
    9728, 9729, 9730, 9731, 9732, 9733, 
    10181, 9734, 9735, 9724, 10370, 10372, 
    10374, 10376, 10377, 10378, 10379, 
    10380, 10381, 10371, 10373, 10375, 
    10387, 10395, 10390, 10394, 10393, 
    10392, 10386, 10389, 10388, 10637, 
    10638, 10639, 10640, 10641, 13013, 
    13014, 13015, 13016, 13017, 13018, 
    13019, 13020, 13021, 13022, 13023, 
    13024, 13025, 13026, 13027, 13028
  ) 
  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 0.00087

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": 128,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (10708,10709,10710,10711,10712,10301,10302,10303,10304,9945,10601,9727,9728,9729,9730,9731,9732,9733,10181,9734,9735,9724,10370,10372,10374,10376,10377,10378,10379,10380,10381,10371,10373,10375,10387,10395,10390,10394,10393,10392,10386,10389,10388,10637,10638,10639,10640,10641,13013,13014,13015,13016,13017,13018,13019,13020,13021,13022,13023,13024,13025,13026,13027,13028) 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)"
    }
  }
}