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 (
    1566, 2282, 2248, 1573, 1493, 1574, 1527, 
    1589, 2256, 1709
  ) 
  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 0.00107

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": 20,
      "filtered": 100,
      "index_condition": "cscart_seo_names.object_id in (1566,2282,2248,1573,1493,1574,1527,1589,2256,1709) 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
1493 crush-col.-20 302/307/308/341
1527 gravitaciya-col.-32 302/307/308/343
1566 eskimo-col.01 302/307/538/539
1573 salon-col.05 302/307/373/542
1574 flashback-col.01 302/307/373/543
1589 magnifico-col.04 302/307/535/540
1709 winnie-col.04 302/307/538/553
2248 borneo-col.-11 302/307/308/565
2256 persona-col.-01 302/307/373/566
2282 garmoniya-grafika-col.-04 302/307/535/560