Rename/delete files in Mac OS X save window

If you are talking about operating on files in the folder structure you see in the Save window as if you were working in a Finder window, the answer is no.

The only operation that approaches this is to click on a filename appearing in the Save window, which will then rename the file portion of the filename, and save the file in its native format.

Below I'm saving a TextEdit file, (Untitled.rtf is the default file name & extension):

When I click on the Word document 3D_Course_v2.Doc, the filename changes to match, but keeps the format of the file, as evident by the .rtf:

A quick test in OS X 10.10 shows that you can copy and delete, but not rename files from the save dialog box. Right(control)-clicking on a file brings up the options for Move to Trash and Duplicate. The usual behavior of changing a file name by clicking on the already-selected file does not seem to work as it does in the Finder.