AFAIK you can't save a scene with another name and keep your current scene with the old name, nor save in another folder (project) and keep keep our old project active. You could save and re-save or re-open your scene with your old name, but that would take a while if you're working with a very heavy scene.
It's a pity because I always wanted to save my backups in a fast drive while working in my slow HDD. I used to use Chinny's Incremental save a few years ago. Had some problems but It did the job done most of the time. https://area.autodesk.com/downloads/plugins/incrementalsave_v2_5_and_autosave_v2_5 Now I use my own code to satisfy my own needs. I would share it but it isn't a customizable plugin. I wrote it for an specific project and now I just got used to it. Martin

