I don't see how you can send off without already knowing the players name (and if you do, you don't need to ask for it).
What if that player's name really is Michael Mouse? Extremely unlikely, but possible. That's why we've been told to report whatever name is given and then let them get in bigger trouble when the player carded isn't a registered player at the club.
Edit to add: Reminds me of the time Sanchez Watt was sent off for repeatedly saying Watt to the referee when asked what his name was