Had this same issue, posted an answer to another user withe same question here
I've copied and pasted that answer below:
"Had the exact same problem. I went through three different Apple Support people before they handed me off to advanced support.
What ended up working was restarting the computer and going into recovery mode (immediately after powering on push and hold both the "Command" and "R" buttons together until the Apple appears, then let go). Once in recovery mode, in the upper-left corner menu, choose "Startup Disk" and if you see a disk image with OS 10.15, that means that Catalina has successfully installed, but just needs to restart properly. Select the 10.15 disk image, then use the restart option. If this problem is the same as mine, it will finish the install then start up normally.
With regards to the error message, the advanced tech said something to the point that the OS is trying to install a copy of itself over the existing copy that is currently installing (or something like that - this was a couple weeks ago), and since that's "impossible" (direct quote) it causes the error.
The odd thing is that it did the same thing with the OS Catalina supplemental update that came out a few days ago, with the exact same fix, so unfortunately it seems like this is going to be an issue with my computer for as long as I have it. My guess it's likely hardware related, as I have an older 2016 MacBook Pro; but if anyone else has theories - I'd love to hear them.
I really hope that helps, it was extremely worrying when it happened to me."