In the last week or so, when I upload photos to Lightroom, instead of uploading in the Navigator in date order, they are all going into the 2020 folder. So instead of going into a folder under 2020, say 2020-09-16, they just go into the folder where I can see all 2020 photos in chronological order. I've checked my settings - with my camera plugged in, import selected, it says From: (my camera model) - Copy - To: Ext HD. I normally Rename File with the current date, next to Custom Text and hit import.
Apparently you are referring to Lightroom Classic. This is the forum for Lightroom, the cloud version. But to briefly answer your question, not only do you want to rename your files if that is your desire, you also need to go to the right-hand panel and choose the precise destination for your images, including choosing the external hard drive, the parent folder, and if you want the images in a date formatted subfolder then you need to choose the format for that subfolder. You are in control of all that, but you must take control and set that up before you initiate the import.