Is there a way to log what changes a user makes when they log in to the designer

Probably not. The other day I saw a post where someone asked the person creating a new Appian user account was tracked and the response was no, it was not being logged. If new licenses/account creation isn't being logged, I doubt individual designer changes are. Publishing a model saves the editor with the version number and date/time. Creating a new model and saving shows the creator, but individual saves I made today to a test model do not show a running tally.