After following the ISO test case "Install (Auto-resize" and rebooting, the subsequent GRUB displayed with the two O/S's should that the new Ubuntu Budgie install was displayed in GRUB as "Ubuntu".
The other Ubuntu Budgie install is shown as "Ubuntu Zesty Zapus"
ProblemType: Bug
DistroRelease: Ubuntu 17.04
Package: ubiquity (not installed)
ProcVersionSignature: Ubuntu 4.9.0-12.13-generic 4.9.2
Uname: Linux 4.9.0-12-generic x86_64
ApportVersion: 2.20.4-0ubuntu1
Architecture: amd64
CurrentDesktop: Budgie:GNOME
Date: Wed Jan 25 19:44:27 2017
InstallCmdLine: boot=casper only-ubiquity initrd=/casper/initrd.lz quiet splash ---
InstallationDate: Installed on 2017-01-25 (0 days ago)
InstallationMedia: Ubuntu-Budgie 17.04 "Zesty Zapus" - Alpha amd64 (20170125)
SourcePackage: ubiquity
UpgradeStatus: No upgrade log present (probably fresh install)
Just a guess, but maybe this could be handled in os-prober.
My initial thought is if grub could check whether a specific desktop meta-package is installed and use that name instead of Ubuntu. I think "Ubuntu" should still be the name if more than one metapackage is installed instead of trying to pick a name.