Should I overwrite my entire backup or modify the original?

[doofmaczemy]

It's high time i made a second backup, so i thought i would take
the opportunity to learn to do it the right way..
The problem I have is that I have not just made changes within files/documents/folders, etc., but changes to names of files themselves.

Therefore I feel that a complete rewriting of a new backup over the old one is in order.. i am suspicious of what happens when you just make "incremental backups" i think they are called.

That is the extent of my knowledge.
So I'm not s ure how to do this but any guidance would be appreciated.