It is called package name what you are using as a main parameter for pkg-config, and then applying --cflags or --libs, etc one just accesses the parameters specified and evaluated from the corresponding package config file ([some_package_name].pc, a.k.a pkg-config metadata file) that was found in pkg-config search paths.
And yes, there is no rule how package name relates to library name. Typically it's either library name without lib- prefix or just the whole library name. I found the following in pkg-config guide:
A common choice is to match the library name to the .pc name.
For instance, a package installing libfoo.so would have a
corresponding libfoo.pc file containing the pkg-config metadata. This
choice is not necessary; the .pc file should simply be a unique
identifier for your library. Following the above example, foo.pc or
foolib.pc would probably work just as well.
However, you can list all available in pkg-config search paths and find out the correct names before using them in Makefile:
$ pkg-config --list-all | grep dlib