No not at all, you can rename that .aprx without breaking any links to your data. Obviously if you changed the name of the folder that the .aprx is in, that would then break the source links to the data in the .aprx (which isn't really a big deal anyway to fix for a small amount of layers).
to answer your question, yes just go to the folder location and change the name of the .aprx project file (perhaps try it out by making a copy of the folder first if you're unsure).