I've seen some members of the family use only the
von and I thought it was for anonimity purposes or simply because it's too long to write out.

For instance on thefacebook, there are some of the younger Liechtenstein royals who go by von Liechtenstein. Also, I've seen Wenzeslaus use von Liechtenstein professionally.
Also, I wonder if someone loses his Prince title and becomes a Count, does he still retain the von und zu?