Other mistake: When the cons are drinking beer on top of the roof, the man that finished his bottle gestures for another. The guy takes out an already-opened bottle of the bucket horizontally, the beer should've poured out.
Other mistake: When the warden is questioning the night guard in Andy's cell the morning-after the escape, he rips the clipboard out of his hand and hands it to Hadley. The pencil is stuck to the paper but is not under the clip. The pencil would have flown off.
Chosen answer: He probably only knows the name. He doesn't want to know anymore, so he can pin the blame on Andy should anything go wrong. He no doubt hasn't even considered that Andy might have ID so he can access the accounts after his escape.
Grumpy Scot
Also, Andy indicated that the deposits were night deposits, which were in envelopes. So, the warden may not have known the "Randall Stevens" name.