Be careful when you come across them, because all these terms mean "called" in the sense of "alias".
Here in Westphalia, you often find them when you look up old records, especially when you're dealing with families who owned a farm.
When a farmer died without a male heir, his daughter would inherit the farm. It was important to keep the farm's name, so the daughter's husband would from that point on be known as for instance "Schmidt genannt Möller" (which would translate to Smith alias Miller").
It happened in my own family even in two consecutive generations:
My 3x-great-grandfather was Johann Heinrich Schwentker. He was born in 1816 to his parents Anne Marie Schwentker (1783-1856) and Johann Heinrich Panhorst genannt Schwentker (1766-1836).
Anne Marie's parents were Catrina Ilsabein Schwentker (1751-1803) and Wilhelm Henrich Deppermann genannt Schwentker (1750-1806).
So in these two generations, the property was handed down through the female line. I guess that is why "Schwentker" is still a common name in my hometown of Werther.
If the name of the farm had played a minor role in peoples' minds those days, Wilhelm Henrich and Catrina Ilsabein's daughter would have been Anne Marie Deppermann, and her son would have been Johann Heinrich Panhorst, which would have meant that I, finally, wouldn't have been born not as Angela Schwentker, but als Angela Panhorst...
Btw, did I mention I'm an only child?
Okay, my part of the Schwentker family gave up farming three generations ago to become craftsmen, but I guess that if I was in the situation that I was the heiress of the family farm and intended to get married, I'd also want make sure that the name would survive.
The problem with the "Genannt" names is as follows: As years went by, people tended to "forget" that the farmer was not born with the name he had used for often enough two or more decades. When you look up the baptism records for the Panhorst-Schwentker children, in most cases their father's name was given simply as "Johann Heinrich Schwentker" with no mention of his Panhorst line at all, aside from one or two Panhorst godfathers.
So if you ever stumble upon one or two of the above mentioned terms... make sure to check the marriage entry. And if there is a marriage index, be sure to check the wife's surname!