Product and version FileMaker Pro 14.0.3 (64-bit)
OS and version Windows 7 Professional
When the list of scripts is longer than "one screen" and you rename a script at the bottom half of the list, the script list scrolls to the top. Rename the script by right-clicking the script in the list and choose Rename. You need to manually scroll down to see the renamed script again.
How to replicate
It does not happen in a newly created database, it seems you need to rearrange scripts and create script folders before it breaks. You need to make script folders, maybe in 2 levels?, and rearrange the scripts. I made a database from scratch with some empty scripts. It worked fine until I started to rearrange them.
Open the enclosed database, open the Script Workspace, and scroll down to the bottom of the scripts. Make sure you got the scroll bar in the script list. Rename the one I have named "CHANGE THIS ONE", the list should scroll to the top loosing focus. Rename the one I have named "THIS ONE WORKS", it works at it should.
Renaming scripts in the same database on OS X works fine.