Do we need to notify Google of a Domain change? Are there any benefits on this? Our website is in the penalty & I can't think of one reason why we would want to notify them that we are changing our domain. Can anyone provide any advice here?
I think Google is smart enough to find it out. If your website is in penalty, then find the reason out and bring the website to normal status.
I think there is no necessity to inform google about your domain Your site may be in penalty for another reason, not for changing domain. Please check your domain last record with current status, so that you can fix if have any issues.
You can tell google about the domain change in webmaster tools if you want, then add a 301 redirect. Why would you want to if you think the existing domain is penalised?
I would suggest that you don't try to go around a penalty but rather fix the problem. Changing a domain name while still having the same problem that brought the penalty will probably not sit well with Google. Don't try to game the system. It's not worth to risk your account getting banned.
there is no penalty by changing your domain name i think so, it is possible that there may any other reason
Well, if you use domain forwarding then I think there is no need to notify google but every moment google is changing its policies. Who knows you might loose all ranking of previous domain. So I think to avoid risk you should notify google about new domain.
If you think this is going to benefit then you must use redirects, but as you said your previous domain was banned, then its better not to use any such thing...
Don't communicate with Google at all, it is useless, just do your job right and it will find out everything it needs.
If you domain have a penalty and you change your domain for that, don't tell Google you make 301 ... Google will see the 301 by himself and if you are lucky, the penalty will leave.