Note that if you're an annual member, you'll need to put your real name back under "Billing" at renewal time for the payment to go through. I don't believe that this affects the name on the forums, though. It was more of an issue when the late lamented BPL store was going--you had to put everything back on both "Billing" and "Shipping" when you placed an order, which meant your real name would sit on the forums for several days.
Actually, you can run but you can't hide. Googling my real name just came up with my town, age, several relatives, several places I've lived before. For 95 cents (sale price!) I could have bought my name, complete address and phone number. For $30 I could get all sorts of info about myself including property records, list of relatives and neighbors and criminal record (haven't even gotten a traffic ticket since 1972). Plus my address and the valuation of my home are there for free. There just ain't no privacy any more!