Welcome to the forum Bananacustard,
The ESA form goes back to ATOS not the DWP the address is on the letter that came with your ESA50 form.
If you cant find the original letter or envelope, they do send a reminder, however you can use this link to find your regional office address from the 'choose location" drop down menu.http://uk.atos.net/en-uk/about_us/locations/default.htm
you could also email ATOS customer relations to check the address of your regional firstname.lastname@example.org
Make sure you make copies of your form and all your supporting evidence, and send it signed for or special delivery so you can track its progress.
I note you have an issue with a name change add a letter with your form notifying them of the change and also send this your local DWP paying office, and make sure you annotate any copies of medical evidence supplied with both names. and always make sure NI is on every page.
Have a search through the forums there is a wealth of information and people going through the same or similar situations who will offer advice and support as they are able.