As Tyler points out, there's no way to do what you require "directly and reliably", since a given FD may correspond to 0 filenames (in various cases) or > 1 (multiple "hard links" is how the latter situation is generally described). If you do still need the functionality with all the limitations (on speed AND on the possibility of getting 0, 2, ... results rather than 1), here's how you can do it: first, fstat the FD -- this tells you, in the resulting struct stat, what device the file lives on, how many hard links it has, whether it's a special file, etc. This may already answer your question -- e.g. if 0 hard links you will KNOW there is in fact no corresponding filename on disk.
If the stats give you hope, then you have to "walk the tree" of directories on the relevant device until you find all the hard links (or just the first one, if you don't need more than one and any one will do). For that purpose, you use readdir (and opendir &c of course) recursively opening subdirectories until you find in a struct dirent thus received the same inode number you had in the original struct stat (at which time if you want the whole path, rather than just the name, you'll need to walk the chain of directories backwards to reconstruct it).
If this general approach is acceptable, but you need more detailed C code, let us know, it won't be hard to write (though I'd rather not write it if it's useless, i.e. you cannot withstand the inevitably slow performance or the possibility of getting != 1 result for the purposes of your application;-).