Q. How do find out which adapters (IDs for adapters) installed in a Linux sever or machine?

A. You need to use lspci command.

lspci is a command for displaying information about all PCI buses in the system and all devices connected to them.

Type lspci -n command to display the IDs for adapters installed in a particular Linux server system.
$ lspci | less
OR
$ lspci -n

-n option shows PCI vendor and device codes as numbers instead of looking them up in the PCI ID database.