I am trying to put a superscript character in AD in the Name attribute, however it displays it as a normal character.

What are the limitations of value for AD Pro

It works for me (Windows Server 2012 R2 domain controllers) and display the info in the GUI as well as in the output of PowerShell command let... Now I'd believe that depending on the client you might have different result... Where do you see the display issue?

The superscript character also displays well in my local testing environment. Maybe share the superscript character that you are using, I will test again with it.
 
Also, as already asked, where exactly do you see this issue? More specific information is required.
 

Regards,

Eth