The forums isn't a place to appeal a ban. We can't review accounts from here and Jagex won't. You can however do so from here...
Appeal A Ban (click me)
follow the prompts there.
As to logging in. Login with the original name you told us here not the one the account is known as now. The login name for the account will never change regardless of the amount of times you change the display name or the registered email address.
When the day becomes the night and the sky becomes the sea, when the clock strikes heavy and there’s no time for tea; and in our darkest hour, before my final rhyme, she will come back home to Wonderland and turn back the hands of time.