It did exactly what it says in the Catalog Upgrade dialog box:
- The converted catalog retains the same name and folder location.
- The previous version catalog was backed up, compressed with the date and time added to the filename, and moved to a new subfolder called Old Lightroom Catalogs. Although that last part is hard to see if the Old Lightroom Catalogs folder name is truncated to fit the folder path in the available space.

After completing the upgrade, including following the prompts for converting my catalog, it still shows I am using a v13 catalog.
By @greggplu
Does that mean it still says 13 at the end of the catalog name? Because they did change that, they no longer add the version to the name. This is a good thing, because lots of long-time users had catalog names that ended like “…v10-v11-v12-v13” This finally puts a stop to that.
I also had the version number at the end of my catalog name, and because of the way Adobe changed the upgrade process, I knew the catalog name would not be altered again. So I used the handy new File > Rename Catalog* command to take the version number out of the catalog name, and that might be the last time I’ll ever have to manage that catalog name.
*For those of you who might say “Can’t you just rename the catalog file on the desktop like you do with other files?” The answer is sure, but you also have to remember to rename all of the associated files like its previews file, Smart Previews file, helper, etc., if present. The Rename Catalog command handles all those files for you.