Well you got the answer.
We will talk about it but for first say it would be no.
Since you are willing to talk about it, these are the reasons in brief I believe that regular users should be able keep a track of premium members name changes:
1) It isn't easy to identify members with changed names when you have signatures and avatars turned off.
2) Even if you have them turned on, if you are away from this forum for a while and come back, those could have changed, making the user tough to identify.
3) I do not believe that this would take away any "privilege" from the premium members.
4) As Litotes
said, I believe it would be fairly easy to do.
(I have continued this conversation here instead of making a suggestion thread about it since I do not wish to make this a long drawn argument. If you still say no, I will not argue further, but I sure hope you think over it.)