Hi MarjonVerhoeven1,
Based on your post, I tested on my end to confirm the behavior, I tried both the methods i.e., Copy form and Duplicate form and in both the cases renaming the form shows the updated name in the All forms list, as shown below.
Please try closing the browser and check the result again, it might be possible it is taking some time to propagate the updated name in the All forms list.
Besides, if possible, please try re-naming another form and check if it shows the updated name, this will help us confirm whether the issue is with the specific form or not. Besides, please confirm whether you copied the existing form or created the duplicate.
Regards,
Neha