What do you call the square badge that would go on the front of briefcases and the like.
The one that is missing in this picture.
I am looking to get a custom on made but not even the slightest idea how.
Name plate?
Find a place that makes trophies, like for high school football, or bowling leagues.
If you are in the US or Canada, your local Things Remembered store has metal plates that can be attached, though with that being a recessed cavity it might be a little more challenging to find a size that will match. Take the case with you, and if one of their standard service plates won’t fit, ask them to look through their replacement plates as well. They can also engrave the plate for you. Plates are self-adhesive; if you want a more secure attachment use a household cement.
I submit that the formal name for that plate is an escutcheon - see Def #3 here:
On a pocket knife, the little metal inlay, sometimes shield-shaped but often rectangular, is called this…