The current directory is a long-standing Unix concept, so you'd have to trace its history back quite far to hear arguments about why it was there. One obvious reason is that relative paths are convenient for all sorts of reasons and they require a point to be relative to, which is basically 'the current directory' in some form.
The kernel knowing the name for the current directory is not specific to current directories; it is part of a general system of caching the name mappings for directory entries ('dnodes' in Linux, a 'name cache' in FreeBSD). Unix kernels added these caches because Unix programs spend a lot of time looking up names, making the operation worth optimizing in general. Once you have a general name cache, you might as well pin the entries for actively used entities like current directories and open files so that they don't get expired out of the cache and you always know (some) name for them.
(One useful complexity of name caches is that you can cache negative entries, ie that a given name is not present in a directory. In the modern Unix shared library environment where shared libraries may be probed for in a whole collection of directories every time a program starts up, I suspect this saves a nice chunk of kernel CPU time.)
The kernel knowing the name for the current directory is not specific to current directories; it is part of a general system of caching the name mappings for directory entries ('dnodes' in Linux, a 'name cache' in FreeBSD). Unix kernels added these caches because Unix programs spend a lot of time looking up names, making the operation worth optimizing in general. Once you have a general name cache, you might as well pin the entries for actively used entities like current directories and open files so that they don't get expired out of the cache and you always know (some) name for them.
(One useful complexity of name caches is that you can cache negative entries, ie that a given name is not present in a directory. In the modern Unix shared library environment where shared libraries may be probed for in a whole collection of directories every time a program starts up, I suspect this saves a nice chunk of kernel CPU time.)