Unlike subversion, git does not have a per-file history. If you look at the commit data structure, it only points to the previous commits and the new tree object for this commit. No explicit information is stored in the commit object which files are changed by the commit; nor the nature of these changes.
The tools to inspect changes can detect renames based on heuristics. E.g. "git diff" has the option -M that turns on rename detection. So in case of a rename, "git diff" might show you that one file has been deleted and another one created, while "git diff -M" will actually detect the move and display the change accordingly (see "man git diff" for details).
So in git this is not a matter of how you commit your changes but how you look at the committed changes later.
