I'm surprised why everybody says it is not possible. It is possible on Linux for non-static functions.
I know at least two ways to achieve this.
There are GNU functions for backtrace printing: backtrace() and backtrace_symbols() (See man). In your case you don't need backtrace() as you already have function pointer, you just pass it to backtrace_symbols().
Example (working code):
#include <stdio.h>
#include <execinfo.h>
void foo(void) {
    printf("foo\n");
}
int main(int argc, char *argv[]) {
    void    *funptr = &foo;
    backtrace_symbols_fd(&funptr, 1, 1);
    return 0;
}
Compile with gcc test.c -rdynamic
Output: ./a.out(foo+0x0)[0x8048634]
It gives you binary name, function name, pointer offset from function start and pointer value so you can parse it.
Another way is to use dladdr() (another extension), I guess print_backtrace() uses dladdr(). dladdr() returns Dl_info structure that has function name in dli_sname field. I don't provide code example here but it is obvious - see man dladdr for details.
NB! Both approaches require function to be non-static!
Well, there is one more way - use debug information using libdwarf but it would require unstripped binary and not very easy to do so I don't recommend it.