I suppose anonymous is anonymous...but why would you want them to be separate?
Unless you're going to be intentionally talking out of both sides of your mouth, or you intend to praise Forum A when you're on Forum A but then badmouth it when you're on Forum B -- why not use the same name?
The single handle or name is already anonymous (as you want it to be) to begin with.
I'd say it's not as sneaky as holding multiple accounts, but it's more honest to use the same name everywhere.