Yes, it's called roaming.
quote:
Originally posted by [url
http://messengersays.spaces.live.com/Blog/cns!5B410F7FD930829E!25206.entry]Roaming[/url] Identity - Your display name follows you any place you sign into. Now your display picture and personal message will follow you too. If you would prefer they stayed in place you can turn this off (Tools->Options->General -> Sign In -> "Use the same display picture....")