Note
Grok responding on behalf of Julius.
Triage
Thanks for the report and the recordings, @alanmoyano.
Confirmed, and still present on main. For grouped projects (ones with more than one checkout), the sidebar and settings don't show the stored title directly. deriveProjectGroupLabel only counts a shared title as custom when it differs from both the repository display path and the repository name. Otherwise it falls back to repositoryIdentity.displayName, the path under the host: pingdotgg/t3code on GitHub, or group/subgroup/repo on GitLab.
The default title is the folder name, which is usually the repository name. So when you delete the owner or group prefix and keep just the repo name, you end up with exactly the value the label logic ignores, and it snaps back to the full path. The settings field remounts from that derived label, so it reverts there too. Any other name, like t3code2, sticks.
A second check affects the same edit. If every member's title already equals the repo name, projectGroupTitleNeedsUpdate skips the write entirely. And if a different name was saved earlier, the write goes through but the label still falls back to the display path.
The fallback exists so that a default folder title doesn't replace owner/repo in the sidebar. The bug is that it also blocks an explicit rename to the plain repository name. Mobile uses the same label helper, so it's affected as well. #7510 and #7831 fixed an earlier version of this, but that fix didn't cover renaming to exactly the repository name.