I suspect you may be running into EFI issues. Under normal conditions, installers will use an existing EFI partition and not create another one, and all installed OSes will use the same partition, including windows. The problem is, this “dual boot” configuration becomes dependent on the already installed oses, and when you remove one, the system suddenly wont boot as it depends on the presence of the old OS. So likely what happened is Neon saw the EFI, saw “valid” data from ubuntu, and used it. But, as you see, that fails.
So, the easiest way to check for that issue is to try to install a truly portable version of Neon on an external drive. Just installing it on an external will not solve the problem, you need to make it actually portable as described below.
To do this, start a live USB session. When you get to the partitioner, disable the existing EFI boot flag on whichever drive it is on using the partition manager by right clicking on the partition, then click properties, and then uncheck the “boot” option. Then create your standard /efi, /boot, /swap, and data partitions on the EXTERNAL drive.
Install Neon, then BEFORE you reboot, reset the boot flag on the old EFI, then start neon from the external drive. If this works, then you have your culprit. Reboot with the external removed, and you should boot to the old EFI as per normal, and have the same issues with “ubuntu” (a properly installed neon will show “Neon” in the grub menu, not ubuntu).
If it is a single boot system, then you can simply delete the existing EFI and boot partitions, and reinstall Neon. If you are dual boot with Windows, then you will need to reset the EFI partition with Windows itself (recovery system), then install Neon as per normal.
Now, I have not tried this on internal drives, but it seems to me that deleting the existing EFI if you have windows installed, should result in grub still seeing the Windows partition and setting up grub properly. Again, I have not tested this as I solo Neon on my PC, but EFI is supposed to be independent of the OS. If you do try this on an internal drive, then ensure you know how to restore the Windows EFI using the Windows recovery system should something go amiss.
See this doc for more info on how to properly set up an portable install for Linux.
How to Create a Truly Portable Ubuntu Installation on an External USB HDD or SSD | Anthony Bouch