The advantages to this idea are clear, but I don't think we can enable thread-title-editing with the current forum software setup. Lacking that, we settle for the 2nd-best choice: Edit the first post (not the thread title) to note that an item is sold or a problem has been settled, and ask a moderator when you want a thread title changed. Such requests should usually be handled quickly.
The best way to ask a moderator for help, which is not obvious, is to use the "Report bad post" feature on any post in the thread, and make your request in the description. You can't report your own post, however (something else I wish we could change), so this method only works if somebody else has posted in the same thread. It seems counterintuitive since the other post isn't "bad", but doing it this way guarantees that any moderator on duty will see it. If you PM a moderator instead, the one you pick might not be the one who would see your message first. And if you PM all of them, it makes more work for everyone involved.