How do I re-name a program?

Simple question.

If it's not possible, then is there a way to make a new program and 'copy and paste' (or an equivilant) the script into that instead?

Hmm. Yes. There is. Use this in the shell.

cp [oldprogram] [newprogram]

Sans brackets. Make sure you are in the same directory.

When done, delete the old program name. And viola.

go to the computer's folder (.minecraft/save/computers/computer #) Then right click the program and hit rename

Well, that's what the rename program is for:
> rename <OldName> <NewName>