When you open up a bank account you provide the bank with enough information to let the IRS know about any deposits such as your SSN number, full name, address etc.
Banks don't usually report an occasional cash deposit of less than $10,000.000 but if you make multiple cash deposits of $10,000.00 or less in a short time then yes those cash deposits will almost always be reported to the IRS and then the IRS will be contacting you soon.
Banks always have to and are required by the Federal Government to report cash deposits of more than $10,000.00 to the IRS.