Thank you for posting this issue.
There was a critical defect for renaming flight plans that existed in version 10.0, but was fixed in 10.1. Have you upgraded to v10.1?
The procedure I'm doing is the following:
1. Flight Plan -> Tap on Name at top -> Edit Flight Plan Name, then "Save/Load => Save current plan" .. this works for me.
2. AND, "Flight Plan -> Save/Load -> Save As => change the name" also works for me.
My tests confirm that this bug was fixed in 10.1.
If have already upgraded to version 10.1, and this issue is still happening for you, please reproduce it one more time, and then do "Menu => About => Send Bug Report" so that I can see the log and look for causes.