To update WD SSD firmware from linux, check this thread: Western Digital Drive Update Guide Without Windows/WD Dashboard - #48 by nos1609
I followed the manual directions (roughly) to update my SN770 1TB:
$ sudo smartctl -a /dev/nvme0n1
...
=== START OF INFORMATION SECTION ===
Model Number: WD_BLACK SN770 1TB
Firmware Version: 731120WD
...