In the output of hostnamectl:
Static hostname would be the name the system might use in its DHCP request, if configured to disclose any name at all. Icon name is just a generic desktop icon name, compatible with the freedesktop.org Icon Naming Specification, to depict the system's role/form factor. For example, it might be computer-server, computer-desktop or computer-laptop. It should not be used as a form of host identification anywhere. Machine ID and Boot ID are basically internal identifiers to uniquely refer to a particular installed OS and its specific boot instance. I don't think there's even a standard way to pass these to a WiFi hotspot.
I would guess that the hotspot will probably use the WiFi MAC address for the actual access control, and the hostname just as a convenient human-readable label for it.
Note that newer Linux distributions will tend to randomize their WiFi MAC addresses for privacy reasons, unless you specifically disable that feature (either for a particular wireless network, or universally). If such randomization is in effect, it will make connections to a WiFi hotspot that uses MAC address whitelisting very difficult.
To disable MAC address randomization when using NetworkManager, you can use a command like:
nmcli connection modify <connection name> 802-11-wireless.mac-address-randomization never nmcli connection modify <connection name> 802-11-wireless.cloned-mac-address permanent
After these commands, the specified NetworkManager connection entry will be configured to always use the permanent MAC address of the WiFi interface in that particular wireless network.
The first command means "stop randomizing the MAC address", the second "don't keep using the last randomized address, but explicitly revert to using the wireless interface's permanent MAC address."
sudo journalctl -b 0 -u NetworkManager. Also do:service NetworkManager status.hostnamein theNetworkManagerlogs is indeed the required name? What aboutIcon name?ip linkand match on that.