No.1 - Lots of new/not so technologically advanced players will have no idea how to rename replays.
No.2 - If you dont minimized/tab out of Demigod after every game, and rename your replays manually then you will get a build up of replays with all very identical names...and you wont remember which one is which.
No.3 - Its not a "feature". You cant put on the back of the game, "Buy Demigod now! Now with extra name-your-replays feature built in!" Its a very basic addition that even the oldest RTS tend to have.
The funny thing is, in the beta when you could save replays (but not watch them) you could actually rename them So they already have this feature somewhere..
It just gives the game that lack of polish feeling and can be quite annoying:
Remind me which one was that awesome game I played the other day...