They don't catch rule violations right away. There are too many performers/members for them to keep an eye on everything and everyone, so things can slip through the cracks for a while. Someone probably reported you and you got brought to their attention, so you were banned. Even if you can get away with breaking rules for a little while, it doesn't mean you'll be able to get away with it forever. Just because someone else can get away with breaking a rule, doesn't give you free reign to do so too. They'll get caught eventually, just like you did. Which is why it's a good idea to research your sites thoroughly before joining, so you know exactly what is and isn't allowed. Though, honestly, I don't know a single live cam-site where incest play is allowed. Perhaps I am wrong! Clip sites are another story - taboo clips are pretty strong on some of them, but not all of them.
Chances are, you prooooobably won't get your account back, even with a name change. Chaturbate bans performers/members ALL of the time for looking too young - even performers who have IDs showing that they are in their late 20s. It doesn't matter. They can't take the risk. From what I've seen, once you're banned, you're usuuuually banned forever. From any account. Even with accidents beyond their control (such as performers looking too young). For an account to break one of their clearly stated rules - I doubt they'll let you rejoin with a name change. They aren't too big on giving second chances - they've got to protect their business and their other performers.