Such a question is very (OS version / GPU hardware / graphics driver) specific as solution varies

If you install https://extensions.gnome.org/extension/120/system-monitor/

there is a GPU setting in Preferences -> DisplayStyle -> both

________________ Only Nvidia GPUs supported so far ________________

Currently on 19.04 here is an error with above install here is work around ... download https://github.com/paradoxxxzero/gnome-shell-system-monitor-applet/archive/master.zip

which will give you ~/downloaddir/gnome-shell-system-monitor-applet-master/[email protected]/

cp -rp ~/downloaddir/gnome-shell-system-monitor-applet-master/[email protected]  ~/.local/share/gnome-shell/extensions

so it results in

ls -la ~/.local/share/gnome-shell/extensions/[email protected]/

install upstream packages

sudo apt-get install chrome-gnome-shell    
sudo apt-get install gir1.2-gtop-2.0 gir1.2-networkmanager-1.0  gir1.2-clutter-1.0

to engage issue alt-F2 then type r in popup

If it's the same tools as under Linux, the program you're looking for is probably nvidia-smi.

• For Nvidia GPUs there is a tool nvidia-smi that can show memory usage, GPU utilization and temperature of GPU.

• For Intel GPU's you can use the intel-gpu-tools.

• AMD has two options

  1. fglrx (closed source drivers):

      aticonfig --odgc --odgt
     

  2. And for mesa (open source drivers), you can use RadeonTop

     sudo apt install radeontop
     radeontop
     

^{Source:GPU usage monitoring}