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.