It looks like a Better Finder Reame is your perfect tool for this. Renaming files is exactly what it is designed to do, and I notice according to their home page it supports regular expressions. That means you can probably use something like this as your match and replace patterns to reorder the component parts of the file names.
Just keep in mind, if you have “-” in your first part or second part, and not just separating them, there’s no way for the app to tell which “-” to use.
I don’t use that app, so if you do need help with how to use your app, maybe their YouTube tutorials will help? That seems to be the only online help they list, so if it wasn’t immediately obvious in the app how it works, that is where I would start with teaching myself how to use the app.