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 (
    1588, 2281, 2295, 2470, 2287, 2293, 2289, 
    2296, 2291, 2450, 2288, 2472
  ) 
  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 0.00077

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": 24,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (1588,2281,2295,2470,2287,2293,2289,2296,2291,2450,2288,2472) 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)"
    }
  }
}

Result

product_id seo_name seo_path
1588 magnifico-col.03 302/307/535/540
2281 garmoniya-grafika-col.-03 302/307/535/560
2287 garmoniya-grafika-col.-09 302/307/535/560
2288 garmoniya-miks-col.-01 302/307/535/560
2289 garmoniya-miks-col.-02 302/307/535/560
2291 garmoniya-miks-col.-04 302/307/535/560
2293 garmoniya-miks-col.-06 302/307/535/560
2295 garmoniya-rogozhka-col.-01 302/307/535/560
2296 garmoniya-rogozhka-col.-02 302/307/535/560
2450 luna-col.-01 302/307/535/580
2470 intellect-col.-01 302/307/535/586
2472 intellect-col.-03 302/307/535/586