I would like to read the function name on the stack element i. How can I read the name?
It looks like you're confusing the C API's stack with the interpreter's runtime stack. They're different animals :)
The stack exposed in the C API is basically just a mechanism for passing arguments to C functions -- that's the stack you're interacting with when you call lua_iscfunction. In the context of the C-API's stack, functions don't have names. They're just pointers.
lua_getinfo, lua_getstack, and luaL_traceback are all tools for analyzing the runtime stack. They're what you want to use to get a string representation of Lua's execution state.
-Sven
