After saving a new file using the “Save As…” menu item in NastPad, the filename in the active tab changes to the newly saved filename (this is a normal response). However, after the first new edit is made, the filename in the active tab changes back to the old filename from before the save (this is abnormal).
I do not know of a current workaround for this bug.
Unfortunately ‘Save As…’ functionality in beta v0.2.1 was broken. The only work-around is to copy/rename files outside of NastPad. It has already been fixed for the next beta, which will be released within the week.