Renaming files with Bash, removing prefix and suffix

I want to rename a bunch of files using bash, transforming this file pattern:

prefix - name - suffix.txt

Into this one:

name.txt

For that I wrote the following script:

find . -name "*.txt" | while read f
do
  mv "${f}" "${f/prefix - /}"
done

find . -name "*.txt" | while read f
do
  mv "${f}" "${f/ - suffix/}"
done

It works, but I'd like to perform the renaming using a single loop. Is it possible?