To get a (new) file descriptor to do anything with you must first call open()*, which takes a filename. So yes, to open a file, you need a filename; the act of opening a file creates a file descriptor to represent that, the same way that running a program creates a new process ID to represent that.

Files are rather different from processes though, in that the PID is fundamental, and systemwide. The filename a process was ran with really isn't relevant since
a) If you have 4 xterms doing different things, you can't tell them apart by what file you ran
b) Lots of processes clone themselves, instead of loading new programs

So the PID is really the only way to identify processes. Commands like killall just trawl through the system's big list of PID's for you.

It's the files themselves that're unusual, and the ways you can use them, not the ways they're opened. There's several kinds of files:
You can also use FD's that have already been opened for you. The FD's 0, 1, and 2 are usually provided for you, where 0 represents the input stream(keyboard, for a console), 1 represents the output stream(the console display, for a console), and 2 represents error message output(also the console display). You can rearrange them how you please, having input coming from a file instead of console and having output going into a file or into another process etc etc etc.

* Okay, socket() and pipe() make FDs too, but have nothing to do with files on disk.