When you erase the drive, you can assign whatever name you wish. The suggestion to rename the drive is there to help you tell the two apart, but it's a convenience, not a necessity.
I've renamed some and just left some alone; performance was not impacted.
Assuming you successfully create an external boot SSD, If you choose to, you can use the internal drive as storage only by erasing it. Renaming it to reflect that is suggested, again for ease of identity. I usually rename it something like "[computer name] Internal Storage-500" for a 500GB internal drive.
"sent the logs". Sent what log, to who and for what purpose?