Is there a way to identify the a user in a web request?

In most communication protocols it's possible to specify a sender
For example, when I send a letter I can write my address on the back
When I make a phone call, it's possible to have "caller display" to see
who's calling
When sending an email I can see who the email is from
But on the web, it's not obvious how to do this
Does anyone have a solution to this, or why it may be a bad idea?