The new Open/Save dialog in Toad 12.1 and above support renaming favorites, whereas the old style dialog doesn’t. For Toad 12.5 and above, we've defaulted to use the old-style dialog, unless you imported your user settings from a prior version. It's possible something may have gotten out of sync on your user settings.
First, check the drop-down itself to make sure your favorite folders aren't appearing in the drop-down list. A favorites folder isn't selected by default in that drop-down box. If it isn't appearing, double-check your options to make sure it's appearing here:
If you'd prefer, you can also check to make sure it's appearing in the new style dialog, by selecting the "Toad World" Script Repository option here:
You don't have to use the Toad World repository to use the new style dialog. If it still isn't appearing, check your Toad.ini file. There's a parameter under your [Settings] section named "CommonDialogFavorites", which is a comma-delimited list of favorites. Those entries should appear in your favorites drop-down, or in the favorites tree of the new dialog.
Let us know if you continue to experience problems with this.