Thanks for providing this video.
To clarify, in the video you are saving a Program, not a Preset. I cannot reproduce this issue, when I type in a new name and click away from the box, the new name remains.
If you’d like to save a Preset, that is, just the parameter values for PitchFuzz, click the 3-dot icon next to the preset and select “Save to Library”.
If you save a Program using the save button in the top right corner, when you load this Program again, you should see the exact values of both Preset A & B.
Is this not happening? It’s not clear from your video if the parameters are being saved or not.