That's why nicknames would be visible only to the person who put them. For example, If I put a "nickname" to, say, you, I'd be the only one to be able to see it. Another person could do the same and only see the nickname they gave you and so on.
I don't know if a thing like that can be implemented in the forums since the nickname on the forums would be server-side while Steam does it client-side, I believe.
That depends. If nicknames are implemented so only the person who puts it can see it, then there's no point in making it permanent. But if it's visible all across the forums, why not?