mojave install issue

I have a 2013 IMac which means it is not compatible for the new Sur upgrade. To access the upgrades for some of my apps I now have to upgrade from High Sierra to Mojave as the latest available to me. I downloaded the software and installed but it wouldn’t allow me to install directly onto the Mac and would only give me the option of using one of my external hard drives which was fine and it installed well although it seemed like it had to be a clean install (I would have preferred an over write). The problem is that it is now using this external drive as the start up which tbh is not ideal and is very slow. How do I get it to install on my Mac start up disk instead? And if you know how I can do it without doing a clean install as well that would be great. I have restored back to HS for the moment until I can get this figure out.