Final answer:
The essential details to provide within a month of opening a bank account are the name of the bank and the account number, as these pieces of information are crucial for identifying and accessing the account.
Step-by-step explanation:
After opening a bank account, the information that should be provided within one month would usually include: Name of the bank, the account number, and the account name. However, if the question specifies that only two pieces of information are required, the most essential details to provide would be the name of the bank and the account number. These details are critical as they uniquely identify where your account is held and how it can be accessed or referenced in financial transactions.