The GNOME Shell search results are forwarded from the results of
GLib's g_desktop_app_info_search() function, which matches the
Name, Exec, Keywords, GenericName, X_GNOME_FullName, and Comment
keys from desktop files[0].

Since Evince is now named "Document Viewer", a query for "evince"
would match the "Exec" key and present the application in the search
results as expected. Unfortunately that doesn't happen for Flaptaked
Evince, which would get its desktop file "Exec" key overwritten to
something such as Exec=/usr/bin/flatpak run --branch=stable
--arch=x86_64 --command=evince org.gnome.Evince --new-document

This way, searching for "evince" when only the Flatpaked version
of it is installed returns no results. Searching for "Document
Viewer" presents the application as expected.

Its been proposed in GLib to parse the "Exec" key for searches
but that was rejected[1] because it would imply establishing an
API which assumes that the command line behavior of Flatpak would
be stable/never-change.

A fix was proposed in Flatpak directly[2] but it was rejected,
leaving us with the only option of adding the historical/legacy
application names to the "Keywords" key in their desktop files.

Many users, such as myself, have the "muscle memory" of search
for the old application's name, such as "evince", "totem", "gedit".
Although I agree that the new names should be presented to new
users and that the old ones shouldn't be visible in UI, it makes
sense and little effort to support the search for the old names IMO.

I proposed the same changes in "gedit"[3].

[0] https://gitlab.gnome.org/GNOME/glib/blob/master/gio/gdesktopappinfo.c#L378
[1] glib#1706
[2] https://github.com/flatpak/flatpak/issues/2749
[3] gedit!44