If someone has the power to ban you then they are allowed to do so otherwise they wouldn't have that power in the first place, even if they ban you for absolutely no reason at all it's their choice and their right to ban you, even if they want to ban you because they don't like your nickname it doesn't matter, it's their right to ban you for whatever they like.
I'm perminently banned from a channel for saying i like wmp better than winamp, whether it's unfair or not, i don't have a right to evade the ban, sure i could evade it, but as watchdog said it would make things worse.
Just wait the ban out or try contacting them and asking them to either remove it or ask if they can make an exception.
If you decide to contact them, remember to be polite, don't say anything like "unban me now you little <something>, i've done nothing wrong"
Until then, find another place to chat.
There are thousands of servers out there, whether it's as good as the one you were banned from or not, it should be fine to use until you are unbanned.
If they decide that it's a perminent ban, just put it down to experience and find another server to chat on perminently.
Don't bother evading the ban, because they will see that you've evaded it sooner or later and then they will just ban you again, it's much easier and better to just cooperate with them than trying to get around it.
