Error sending mail with Civimail
two possible sources of the error:


you have changed something in the configuration of your mail accounts in civi (or didn't finish the config previously), check the documentation, the "localpart" should not be empty but name of your bounce mailbox (eg if your mailbox is bounce@example.org, it should be "bounce+")
civimail relies on a trick that most servers implement: if you send and email to bla+whatever@example.org, it will automatically be understood as an alias of bla@example.org


It seems that you need to at least fix the localpart, as your new mail server is more strict and better at catching configuration problems