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 (
    2395, 2597, 2404, 2596, 2390, 2405, 2094, 
    353, 355, 2392
  ) 
  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 0.00057

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 (2395,2597,2404,2596,2390,2405,2094,353,355,2392) 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
353 160x230-basalt-773-s-677230 302/303/321
355 160x230-apatite-342-s-497140 302/303/321
2094 belgiyskiy-kover-160x230-prisma 302/303/306
2390 tureckiy-kover-botanica-bone-black-160x230 302/303/304
2392 tureckiy-kover-elegant-bone-bone-160x230 302/303/304
2395 tureckiy-kover-lama-ii-bone-black-160x230 302/303/304
2404 tureckiy-kover-wave-160x230 302/303/304
2405 tureckiy-kover-zebra-bone-bone-160x230 302/303/304
2596 belgiyskiy-kover-antique-200x290 302/303/306
2597 belgiyskiy-kover-florense-200x300 302/303/306