Go to Settings > General > About and you should get a prompt that their is a carrier profile update and it will then change to EE. I was on iOS6 GM and that worked for me.
Installing iOS6 must trigger it to check for a carrier profile update.
On the Wife's 4 it has profile 12.0 .... Did not prompt me and still says Orange.... What version of the profile do you have now that EE is displayed?
I seem to remember having to do it with the iPad 3 to unlock the hotspot feature on the Three SIM