You can throw away old credit card statements if you no longer need then credit card statements.
However before throwing away the old credit card statements you should first shred them up or rip them up in small pieces to prevent someone from stealing your identity.
Also use a black marker to mark out any identifiable information on the credit card statements even before tearing or shredding as they can sometimes be pieced back together to get your identity.
It is bad to throw away mail with your name on it as throwing mail away with your name on it can lead to identity theft.
Any mail that you want to get rid of with your name on it should be shredded or destroyed to prevent identity theft.
Sometimes identity thieves will go through garbage and look for mail and documents to steal your identity with.
I always shred any information up and mark out any personally identifiable information on any mail.
Even if it's junk mail that has your name on it you should always shred it or rip it up or even burn it to prevent it from getting into the hands of identity thieves.
Identity thieves have also been known to piece together torn up mail and even shredded mail to try and get information.
Burning the mail or documents if possible will prevent all of that.