Not sure about easier, but a simple Perl script could probably do this pretty easily. Once you managed to get the regex pattern correct anyway.
Something along the lines of telling it to look at every file in a directory, and scanning for KB and then some arbitrary amount of numbers, followed by a period. Then storing the KBXXXXXX into a variable and renaming the file, starting with that number.
The program itself probably wouldn't be more than a dozen or so lines. It's just debugging that regex pattern that would probably be the annoying part. And learning enough Perl and Perl-style regular expressions. There might be a mass/bulk file renaming program out there that will accept Perl-style regexs, so that might be a good shortcut.
I use the Admin Options at the Update Center to separately download the updates so I can install them later and have backup copies of everything so after a format I don't have to get them all over again. I've done this for years going back as far as early W98FE.
Something that has always irritated me and continues to do so is that MS insists on putting the KB number at the end of the description of the file rather than at the front.
It's much easier for me to make sure I haven't missed any updates by scanning the KB number quickly from the list of those files inside the folder where I keep them. However, Windows Explorer lists them all alphabetically based on the description. This forces me to rename every single file by manually putting the KB number at the beginning of the line, close that folder, and then reopen it so they automatically then fall into line numerically instead.
Is there an easier way to do this mass change when I'm dealing with over a hundred files? The only other option I've found which is just as time consuming is to use the "find" option within the folder each time I need to get a new (or more than one) update.