OK all!

I need some help on cookies.
I need a cookie system that can recognize a user, the next time he visits the web site the site recognizes him and welcomes him, for example: "Welcome back, Joyce Beringer!" Now I know it does'nt always work because not all users have their personal info open for cookies to retrieve them. But I'd like a cookie like that around.
Did I explain myself ok?
Is it possible? Help is welcomed with open electronic arms!