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 (
    15745, 15746, 15743, 15738, 15739, 15740, 
    15741, 15742, 15736, 15737, 10668, 
    10669, 10670, 10671, 10672, 10673, 
    10674, 10675, 10676, 10677, 10678, 
    10679, 10680, 10681, 10682, 10683, 
    10684, 10685, 10686, 10607, 10608, 
    10609
  ) 
  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 (15745,15746,15743,15738,15739,15740,15741,15742,15736,15737,10668,10669,10670,10671,10672,10673,10674,10675,10676,10677,10678,10679,10680,10681,10682,10683,10684,10685,10686,10607,10608,10609) 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)"
    }
  }
}