Check which you you have:
systemctl status display-manager.service
Tested on Ubuntu 23.10 I see:
● gdm.service - GNOME Display Manager
     Loaded: loaded (/lib/systemd/system/gdm.service; static)
     Active: active (running) since Sun 2023-12-24 10:34:50 GMT; 23min ago
    Process: 1827 ExecStartPre=/usr/share/gdm/generate-config (code=exited, status=0/SUCCESS)
   Main PID: 1850 (gdm3)
      Tasks: 4 (limit: 71817)
     Memory: 6.8M
        CPU: 119ms
     CGroup: /system.slice/gdm.service
             └─1850 /usr/sbin/gdm3
which means I have GNOME Display Manager.