Easy peasy, lemon squeezy!

Assuming bash is your default shell:

Editing the bashrc file in Elementary OS
  1. Edit ~/.bashrc in your favourite editor. This file is located in the root file system, not the Home folder. You may need to open as root, but only if the icon shows a padlock or no entry symbol.
  2. Add a new line with “neofetch” in it (without the quotes), towards the bottom.
  3. Save the file, exit the text editor and restart Terminal.
.bashrc in Code
.bashrc in Code
Neofetch