That does work, but then you have some possible housekeeping issues once you get there. If it has the same name, you have to tell it to replace. If you happen to work on more than one project that day, then you have to repeat that with each project, and make sure you file each one in the correct folder.
There are some 3rd party programs that have 1-button click saving of everything to the correct folder/subfolder on your external drive. I use one called SyncBack Free (by Two Bright Sparks). I like the ability to just click once at the end of the day, and not have to worry about all that other stuff. It obviously takes a little setting up to start, but after that it’s pretty mindless … which is what I need at the end of a session!