I know that this thread is old, but it's the first hit that Google finds when searching for mirc nick alert script.

Here's a script that creates a Desktop Window when somebody mentions your nick on mIRC channel window (Nick alert script).

Every time someone mentions your nick, new entry is added into a single Desktop Window. In case someone needs it, here's the script code:

on *:Text:$(* $+ $me $+ *):#: {
  if (!$window(@mIRC-NickAlert)) { window -mdk0 @mIRC-NickAlert }
  window @mIRC-NickAlert
  aline @mIRC-NickAlert 3Network: $str($chr(160),8), 6 $network 
  aline @mIRC-NickAlert 3Channel: $str($chr(160),8), 8 $chan 
  aline @mIRC-NickAlert 3Nick: $str($chr(160),14), 12 $nick 
  aline @mIRC-NickAlert 3Date & Time: $str($chr(160),2), 4 $+($date(yyyy mmmm d) ,$chr(32),2 $chr(40),$date(dddd),$chr(41) ,$chr(32),10 $time )
  aline @mIRC-NickAlert $crlf
  aline @mIRC-NickAlert 13T e x t: $str($chr(160),12), $1-
  aline @mIRC-NickAlert $crlf
  aline @mIRC-NickAlert 5-----------------------------------------------------------------------------------
  aline @mIRC-NickAlert$crlf

Here's how the nick alert script looks in reality: