Sorry, it's "%{reply:User-Name}". From man unlang about strings:
"Double-quoted strings are expanded by inserting the value of any variables (see VARIABLES, below) before being evaluated. If the result is a number it is evaluated in a numerical context.
..
Single-quoted strings are evaluated as-is. Their values are not expanded as with double-quoted strings above, and they are not interpreted as attribute references."
I got it to work, you were right on target about the double-quotes. My real problem was that I was simply pointing to the wrong thing. My original block was reading
update outer.reply { User-Name := "%{reply:User-Name}" }
That returns empty, since the inner reply does not contain any User-Name information. The correct block (which is working now) is:
update outer.reply { User-Name := "%{request:User-Name}" }
So, everything seems fine now.. Thanks all for your help, especially Kalik.. :)