A domain change on a forum using MyBB... Oh dear. That was a long time ago. Like over 5 years ago and it was the only one I ever did with the speciality of changing the domain of the forum after moving it.
Even if I try to remember I can't really come up with much more information than @
deanhills has already shared. The cookie setting is important. If it is in a bad configuration state you will not be able to login into the forum or the administration panel. It will kick you out instantly after login due to issues with the cookies. That is a issue I can remember that I experienced, too.
I'm not sure if I made any other changes in any configuration files or even the database. Sorry.
I did a few Wordpress migrations with domain name changes and there it was a little more work. You had to change things in the settings and also in the database. That was so... at least when I did the migrations. Also quite a long time ago.
I might not be really helpful here.