Where did the name Originate?

What is the meaning of the name Drost and where did it originate? The Meertens Institute, the organization that looks into questions of names, writes:
“A Drost was someone with an important and responsible function working for a monarch, earl or duke. The family name probably gives a very close relationship to a drost: the first person employed by a drost carried the name Drost, or he was an adopted child or a child born out of wedlock. The highly responsible administrator probably did not carry the family name Drost.”

Variances to the name are:
Dros, Drost, Droste, Drosten, Drostenborg, Drosterij, Drosthagen, Therhaar sive Droste.

Below is listed the number of namesakes according to the 1947 census.

Groningen 155
Friesland 295
Drenthe 207
Overijssel 234
Gelderland 531
Utrecht 548
Amsterdam 262
Noord-Holland 210
Noord-Holland totaal 472
Den Haag 105
Rotterdam 75
Zuid-Holland 154
Zuid-Holland totaal 333
Zeeland 20
Noord-Brabant 64
Limburg 51
Totaal 2910