I must add a caveat to this thread, whilst connecting with dial up, your IP address will still be recorded and if you cause any offfence you can still be reported/traced back via the dial-up address you used.
IP addresses are there for a reason and if you do something under another IP that causes offence then you can still be reported and if serious enough tracked back. Afterall there does have to be some record somewhere in an attempt to protect our kids from the likes of paedophiles etc.
On top of that, if discovered, then most forums will take a stern view of 'multi-iding' and ban any users caught doing such thing.
There are some forums that will approve their staff or certain members a 'play name'* but it is usually in the case of if say normally posts in an official capacity on the tech type boards, but wants to let their hair down a little in chitchat... on the provision that they dont attempt to mislead anyone.
*just to clarify
- its not something done on this site.