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 (
    1172, 1173, 1175, 1176, 1728, 1404, 1178, 
    1179, 1180, 1706
  ) 
  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 0.00072

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "14.01"
    },
    "table": {
      "table_name": "cscart_seo_names",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "dispatch"
      ],
      "key": "PRIMARY",
      "used_key_parts": [
        "object_id",
        "type",
        "dispatch",
        "lang_code",
        "company_id"
      ],
      "key_length": "210",
      "rows_examined_per_scan": 20,
      "rows_produced_per_join": 20,
      "filtered": "100.00",
      "index_condition": "((`zdrowy_db`.`cscart_seo_names`.`object_id` in (1172,1173,1175,1176,1728,1404,1178,1179,1180,1706)) and (`zdrowy_db`.`cscart_seo_names`.`type` = 'p') and (`zdrowy_db`.`cscart_seo_names`.`dispatch` = '') and (`zdrowy_db`.`cscart_seo_names`.`lang_code` = 'ru') and ((`zdrowy_db`.`cscart_seo_names`.`company_id` = 1) or (`zdrowy_db`.`cscart_seo_names`.`company_id` = 0)))",
      "cost_info": {
        "read_cost": "12.01",
        "eval_cost": "2.00",
        "prefix_cost": "14.01",
        "data_read_per_join": "33K"
      },
      "used_columns": [
        "name",
        "object_id",
        "company_id",
        "type",
        "dispatch",
        "path",
        "lang_code"
      ]
    }
  }
}

Result

product_id seo_name seo_path
1172 termoetiketka-30h20-eso-2000etik-84 334/339
1173 termoetiketka-43h25-b-p-1000-h80 334/339
1175 termoetiketka-58h40-eco-550-72-c-p 334/339
1176 termoetiketka-58h40-eco-550-72-b-p 334/339
1178 termoetiketka-58h60-eco-60 334/339
1179 termoetiketka-58h80-eco-350-et.-50 334/339
1180 termoetiketka-58h80-eco-500-et.-32 334/339
1404 termoetiketka-58h60-480-eco-60-10 334/339
1706 termoetiketka-75h120-eco-300-etik-dlya-ozon-1-40 334/339
1728 termoetiketka-58h40-eco-500-60-20-b-p 334/339