Anthem has stated that they will not be calling or emailing clients and you should check their site http://AnthemFacts.com for updates. (why that site is not protected by ssl I have no idea)
If you do get contacted personally it's a safe bet it's a phishing attack.
Our Company is affected and all our interaction has been through HR. I would contact your HR department.
Anthem will not be emailing individuals, but apparently will be sending a snail-mail packet of information including an offer for credit-monitoring services. And they have been contacting, via email, the benefits/HR people of client companies which used Anthem for group health plans for their employees.
(that all comes via my employer, which has been sending me updates about this)
That site is strange - they have a big box saying that no medical or credit card data was compromised, then buried in the body text we find out that "These attackers gained unauthorized access to Anthem’s IT system and have obtained personal information from our current and former members such as their names, birthdays, medical IDs/social security numbers, street addresses, email addresses and employment information, including income data. "
CC numbers are far less important than any of those identifiers - unlike your SSN or address, they're easy to change. Someone with all that info can just apply for their own CC or loan in your name...
If you do get contacted personally it's a safe bet it's a phishing attack.
Our Company is affected and all our interaction has been through HR. I would contact your HR department.