I would like to install Blender on a different disc than C, with no residual files on C at all, because I don’t have any space on my C drive. Is there an option to do that? I tried changing the install directory, but it didn’t work. Thanks.
You can install Blender anywhere you wish if you download it's installer from https://www.blender.org/download/
You need to specify your desired location during the installation:
You can also download the portable version if you choose it from the drop down menu in the middle of the download page:
In that case you can just extract the zip file anywhere you wish and just run it without installing at all.
Like others have noticed in the comments, you probably want to address the issue of low space in your C drive anyway, because many programs including Blender usually use it for temporary storage(in Blender's case even autosaves) and you will experience issues if it's completely full sooner or latter. You can use free tools like SpaceSniffer and similar to find out what uses all your space and BleachBit to help you clean it automatically. You should be mindful of what you delete obviously in order not to lose something that you want to keep.