Is it usual for a program to claim a own user profile to run itself?
As mentioned in other answers, this isn't a regular program. It's a daemon. And, yes, it's perfectly normal for a daemon to have its own user.
Is this actually a good sign, because it adds transparency to what happens anyhow?
Is this actually a bad sign, because such an ad-hoc user can intrude upon other stuff?
It's neither good nor bad. It's simply a matter of convenience. On a Linux system, all processes must have some user. It's not possible to have a process without a user. So, which user? Not root, because you should never run anything as root unless you absolutely have to. You could just pick a user, but what happens if that user is deleted? It's much simpler for the installer/package manager/whatever to just create a user and use that.
Having said that, for some daemons (especially network-related ones), there is some security benefit. If someone is able to remotely compromise a network daemon, they'll (in theory) only have access to files that daemon was originally able to access, i.e. files belonging to that user.
Can I retrieve a list of the programs installed in my computer claiming this right of working with an own user name? Basically, can a user oversee such behaviors?
Switching users is a "right" of every process that's running as root. Since daemons are (typically) started by the system boot procedure, they (typically) start as root, so they're (typically) free to arbitrarily change their own user ids. Even after they drop root privilege (if they do so, there's nothing stopping them from continuing as root), they can retain the capability of changing their user id if they need to. So, no, there's no central information repository of which daemons will change their user id when they start, and which won't.
Though, there is a convention that user IDs less than 1000 are reserved for daemon users. So you could look through /etc/passwd for low-number user IDs.