Maybe slightly sidetracked. But the point being if you're in prison, you're going to be end up being identified before you go in. Once you're in, you're likely identifiable to prison staff and police at that point. IRL you'll have an Arrest Summary and Disposal on your PNC record. Your issue was police knew who you were, without you giving the details but if you're within HMP's 4 walls is it reasonable to say you would have been put in there without police knowing who you are? I don't think so.
Adjusting/creating a rule that means you can remain unidentifiable as part of your character at this stage of the justice system firstly doesn't make sense, and just opens up the opportunity for poor balance (as it will just get over used, just like everything else on the server that's 'overdone' or 'overused' that throws things out of balance) in my opinion.
I am 100% supporting your efforts of character avoiding being identified up to the point your arrested, but there is obviously a point between arrest and prison where more would happen IRL to identify you, which is not available in game and some artistic licence needs to be considered on what would happen here.