DemoRecSpectator is a serverside demo recorder and you can't do anything with that unless you're the server admin.
Go to UT2004/System and open User.ini go the DemoRecording section and change the mask.
[DemoRecording]
DemoMask=%d-[yourname]-%m-%t
That will put the date, your name, the map, and the time as the file name. Then, in the same file, bind a key to demorec and another key to stopdemo.
N=demorec
M=stopdemo
Push the proper button to start and stop the demo when needed and the mask will take care of naming it.