When any changes made to our profiles in chatter that is displayed on our profile saying " This person has changed his name " so is there a possibility that we could delete this message in chatter ???
No u can't delete them, but u can block them to create whenever u update your profile from feed tracking settings
setup > customize > chatter > Feed tracking
click on User object and untick all checkboxes then save.
remember: this will not delete your existing feeds but now it will not create feeds whenever u update your profile.
take a loook at http://wiki.developerforce.com/page/An_Introduction_to_Salesforce_Chatter for more info.