The best approach for me is to let google know that your good name website will be the one carrying on its predecessor authority in a gradual way.
Start by notifying google that you will be changing your domain. Use this tool and procedure. I would suggest you do this by temporarily removing your current good domain name content completely, save your unique content URLs and HTTP 302 to a page with a message similar to:
section/content under maintenance comeback date or get notified.
Then, gradually start restoring your content by section/group/etc and at the same time removing the 302s as you go.
For those old domains URLs, specially the ones with backlinks, implement HTTP 301s.
Also you need to get, as much as possible, your old domain social proof, directories, citations and any other references updated to the new domain when possible.