There is a a deployment tool for linux on GitHub. While not perfect, it is linked to from the Qt wiki. It's based conceptually on the Qt Mac Deployment Tool and functions similarly by providing an AppImage.
Given that a desktop file should be provided with an AppImage,
linuxdeployqt can use that to determine the parameters of the build.
Where the desktop file specifies the executable to be run (with
EXEC=), the name of the application, and an icon.