In other cases where we use descriptions, like in PKGBUILD files, the name of the application should specifically not be part of the description.
https://wiki.archlinux.org/index.php/PKGBUILD#pkgdesc

For projects that has several executables or services connected to them, like client and servers or desktops and display managers, including the name of the project is hard to avoid.
"GNOME Display Manager" is a good example of this, even though it should arguably rather be something like "Display manager for GNOME".

If you look at the other .service files on your system, few of the descriptions contains the name of the application:

systemctl --type=service --system

The purpose of a description is to describe what the service is, not to repeat the name of the service, which is already readily available.

Do you have a particular use case where the lack of the name in the description is a problem?

My suggestion is that the description is made even less verbose. Instead of "A secure, fast, compliant and very flexible web-server" I think it should just be "Secure, fast, compliant and flexible web server".

"A" and "very" does not add any information and the hyphen in "web-service" is a spelling mistake.

This is different than PKGBUILD descriptions, because systemd uses the descriptions when starting/stopping services. It's not instantly obvious which web server "Secure, fast, compliant and flexible web server" refers to, unless you remember it.

In either case, the description in Apache's .service file is "Apache Web Server", which is inconsistent with the rest. (Is the reason the same as GNOME?)

Cherokee also uses "Cherokee web server", but that's in the AUR.

For more general things such as polkit, it's not definitely necessary to mention the name of the application itself.

I'd also argue that descriptions like "Manage, Install and Generate Color Profiles" are not good because of how they're displayed:

[ OK ] Started Manage, Install and Generate Color Profiles.

That's out of the scope of this issue, though.

I see. I think systemd is at fault here for choosing to say "Started [Description]", which seldom makes sense.

"Starting [Application name], a [Generic name]" would make more sense, IMO. ("Starting lighttpd, a Web server" for instance).

"Generic name" is already used in .desktop files.

I think both systemd and the color profile description should be fixed in this regard.

The upstream expectation is explicitly documented in the systemd.unit manual:

Description=
A free-form string describing the unit. This is intended for use in UIs to show
descriptive information along with the unit name. The description should contain a name
that means something to the end user. "Apache2 Web Server" is a good example. Bad
examples are "high-performance light-weight HTTP server" (too generic) or "Apache2" (too
specific and meaningless for people who do not know Apache).

The manual is fine, but the choice of the word "Description", with special additional requirements (must look right when following the word "Started") is unusual. For comparison, descriptions in .desktop files does not require this, neither does descriptions in PKGBUILD files. Also, descriptions in other connections often specifically require the name of what is being described to not be part of the description. Requiring the name of the thing being described as part of the description is also an unusual requirement.

Nothing wrong, just unusual. If not directly "at fault", I think it's fair to say that systemd could have chosen different another word than "Description", for clarity, since there are two special extra requirements (must fit after "Started" and must contain the name of what is being described). I agree that this particular bug report is about the problem with the lighttpd description.