I didn’t realize until you posted this that this is a Dolly Parton song. I knew she was a prolific song writer but didn’t know she wrote and performed this one. She has written over 3000 songs so far and is still going.
It’s interesting that this song is not about a romantic relationship. It’s about her professional relationship with Porter Wagner. They worked together for many years. They went their separate ways professionally but left on good terms. This song is about that parting and shows the obvious respect and admiration she had for him.
It is a Dolly Parton song, but before Johny Logan made another arrangement (is this the correct word?) Whitney Houston recorded an arrangement for the soundtrack to the ‘The Bodyguard’.
You could say that he made (or wrote) a new arrangement and then performed it, but I don’t think most people would care about the difference, particularly in this case where they are tied so closely together. My first thought about what you wrote was “Yes, it’s the perfect word.”
Sometimes, though, it is important to identify the arranger separately from the performer.