Discover Savings Account - Identity Theft

[satio]

My daughter has a Discover credit card. Recently she has had someone using her information to open a Discover Savings Account.

It does not appear they are actually logging into her online account but I am not sure exactly what the process i

She gets an alert that the account has been opened and she immediately has called Discover to report the account opening as fraud and to close the account.

She has put locks at the three major CRAs and also with a Check/Savings CRA (the name escapes me at this time).

The most recent attempt was Tuesday August 30th. This comes less than 7 days since the previous attempt last week. There was one other  incident from about 1 month ago. 

She has made it clear that she has no desire to open any additional accounts with Discover and to please mark her profile as such.

She is a young adult managing her own affairs so I have not been party to the actual phone conversations with Discover Customer Service department but the most recent event this week the agent indicated there is really nothing she can do to stop it from happening.

Does anyone have any similar experience with Discover or any other advice as to measures she can take to stop this from re-occuring?

I'm a 57 year old guy who has never had anything similar to this, yes some fraudulent CC or Debit transactions where I replaced the card but not identity theft and someone opening an account in my name. 

I don't accept the customer service staff person's statement that there is nothing more she can really do.

Thanks in advance for any assistance and feedback.

[AndySoCal]

@satio  The only ways  you can open a new account that I know of is either on line or calling Discover.  So my guess is the account was opned on line. I say that I would think there would be a one time pass code sent to verify  the caller plus other standard security questions,.  On line not sure if the one time pass code would be sent or not as a part of that process.  My suggestion would be to have her change her password and user name if possible to her Discover account on a computer that she does NOT normally use to log in with.  I suspect the Discover account may have been hacked. Also have her check her contact information to see if anything else has changed. If she has a credit card lock it or get a new card.