CTRL+F2 for batch renaming Objects is even more useful.
As far as I know there is no shortcut to rename Mesh Data together with the Object Data, but that should be super easy to make in an addon. (I know very little Python and have never written an addon, but I feel confident that even I could write an addon that could do that…)
Personally, I don’t care what the Mesh Data is called, but some people do.
