Right you are Ninna.
I most IP addresses are assigned dynamically by the ISP (each time the user connects) and also wide band addresses are dynamic (though less than dialups), unless one has paid for a fixed IP address -this is considerably more expensive- and I believe it is only available for domains like .com .biz .org and not to individual users.
There are several ways to cheat on the IP address using proxies, such as on-line "anonymizers". These are special proxies that are out there by the hundreds, just to hide the identity of an (usually) offender user.
Sure this site is not using any screening based on IP addresses as they are not effective.
Recently the ISP are forced by law to keep one year registers of their users and the dynamic addresses they have used for each specific connection. But this is related to the war against terrorism and the Mafias, child porno networks and other disgraces of the Internet.
This information is only (at last theoretically) available to a Judge investigating a crime.
PCs cannot be identified as they don't carry a traceable fixed ID number. The industry (I believe the major actors were Intel an Microsoft) fought strongly to get an ID number electronically engraved in each microprocessor. But this was very strongly opposed by Internet users associations (specially in USA) and as far as I know, could not be implemented.
Now, the possibility of having "Multiple personalities" in a Forum or chat space is quite normal and is a feature of the virtuality we enjoy -and suffer. I do not use it, but I find it somewhat appealing.
But lots of people use it frequently and I think it gives some additional possibilities to a site, provided we always take into account that anything said (written) here can have a very different origin than the one declared on the poster's profile or from what we could expect from the aka (not to speak of avatars!)
Those who fear that a person banned because of improper behavior could post again under a different name, should consider that a "person" under an fictitious name is not the real person, but just the image that the real person wants to give to its chosen personality.
So, if a banned guy or girl posts again and that time he/she behaves properly, this is, IMO, completely acceptable.
Second (or later) chances are always good; Internet gives this possibility, that so often is denied in real life.

The inherent anonimity is part of the black legend of Internet but also the basis of the extreme freedom of thought and speech that it permits.
For these reason, all attemps to
<Added>Sorry, just disregard "for this reason, all attemps to".
It comes from a problem with my sloppy cut and paste...