How do I rename a bash function?

Here’s a way to eliminate the temp file:

$ theirfunc() { echo "do their thing"; }
$ eval "$(echo "orig_theirfunc()"; declare -f theirfunc | tail -n +2)"
$ theirfunc() { echo "do my thing"; orig_theirfunc; }
$ theirfunc
do my thing
do their thing