you have to be a little more specific than that.
How do your users log in? Do you use any form of section access?
You will need to set some sort of a trigger to do this.You can probably achieve what you need by putting a trigger on your user selection field that reads the logged in user (osuser function).
Try adding a OnOpen document trigger that will perform a "select in field".
Now you will "only" have to write a little if condition for what the search string will need to be (the search string is what actually will be selected, so here you have to search for exactly the string that you want to select)
As an example, your if statement could look something like this:
Of course, your formula may look a little different, but this should help you get the idea...