I am not familiar with SVN, so I'm not sure if you have a problem, but Git seems to handle renaming well.
After renaming, you must make sure that you have added the file to the Git index, otherwise it will think that you simply deleted the old file and not renamed it.
If you rename the file and make a couple of changes; you may also have renamed one of the #include files. When you commit, you will receive a message like:
rename: MyOriginalFilename -> MyRenamedFileName (99%)
A percentage means that the source file is similar to the new one, so it does not even have to be an exact copy of the contents of this file.
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