How do I show the name of the person a commenter is replying to?

I have a custom theme with a custom comments template. Instead of indenting the list to show which discussion a comment is involved in, I’d like to simply have something like, “John’s response to Jane”.

At the moment my comment form just has the comment author’s name (ie. it just says, “Jane”). That’s fine for top level responses in direct reply to my blog post, but if anyone is responding directly to Jane (for example), I’d like it to read, “John’s response to Jane.”

I’m working on a testing server so I can’t give the url for my site. I hope my question is clear enough so that’s not a problem. If someone thinks they can help but needs more info – like my code – just let me know what you need and how to share it.

Thanks ??