There would be no requirement to rename your USB drive. (the MacOS Base System name is used by the recovery system, so, in any case, would not be one that you would choose.)
Of course, you can name a drive that you have erased -- anything you like. The task of making the bootable USB installer will name it again, so whatever name you choose will ultimately be replaced. And, you can always name it something else, after you create the bootable installer. (I use a name on bootable installers made of special characters and accents, so I have no confusion about the drive when it appears in the middle of some other drives that might have multiple mounted partitions - just something that I do
But, when you have erased the drive, try ejecting that new disk after the format is complete, unplug it from your Mac, then reinsert for a fresh mount. That should help you.
