Just thought I would post:
I did a clean install of Mojave to my 27" iMac yesterday (late 2015 model.)
I was having a minor issue where I couldn't figure out if it was due to the in place upgrade, or a bug in messages.
Anyway, I reinstalled from the recovery partition, I simply reformatted, and everything is good. Turns out I don't think the bug is Mojave specific, as I've seen it before in older versions of macOS.
The problem was: the "Notify me when my name is mentioned" checkbox wasn't staying selected past messages.app being quit, and re-opened.
I did want to mentioned to anyone here planning on doing a clean install, that Mojave takes about the same time as any other version of the macOS to install. I had my Time machine backup ready to go, and manually grabbed stuff from the correct locations that I needed to restore, and it was mostly done in about 2 to 3 hours. This morning, I've mainly spent the time reinstalling the apps from the App Store, and re-entering serials for my commercial products.
Beyond that, starting off clean for another year with Apple.
Also, wanted to mention to this with a Fusion Drive, as long as it's Apple supplied, you won't have any issues with Mojave, and APFS. My drive erased with no issues, and is identified in Disk Utility as an APFS Fusion Drive.
So, While I haven't found what exactly was causing the issue yet, I DO know, that, it wasn't my install of Mojave.