This foal has no name: https://beta-v1.horsereality.com/horses/3626513/foal-doe-3626513

Instead of putting in letters or numbers in the name-bar, if you hit ALT-255, you will create an invisible character that the game accepts as proper naming.

Can be used to create ghost-estate name as well:

The foal still remains clickable (and searchable,as far you remember what it was named) and shows up in conformation shows as usual.

Bonus: it works in forums as well!