Aris Gerritsz was the father of Aerian Arisz and the grandfather of Dirck Aeriansz Aten. The first known generations of this Aten family didn't have a family name at all. Dirck Aeriansz Aten and his three brothers seem to be the firsts who used this name. So it's all the same family, but in the beginning it wasn't called Aten yet. This is quite normal in the Netherlands. In Mediaeval times all names consisted of a first name, only followed by a patronymic. Family names were unknown (of course I don't speak about nobleman, who had some sort of family name already in early times). As population grew, this naming system no longer sufficed to distinguish people, because the variety of first names wasn't very big. For instance, a name like Dirck Jansz, that is Dirck, son of Jan, was likely to appear several times within one village. So people were urged to use some more distinctive name. The first way they tried to solve this, was to use a multiple patronymic (sorry, here it becomes a bit complicated again, but I have to tell you). That means, they took over not only the first name of the father to serve as a patronymic, but took over both first name and patronymic of the father to serve as their own patronymic. For instance, if Dirck Jansz, had a son named Jan, this son could be called Jan Dircksz (Jan, son of Dirck) but also could be called Jan Dirck Jansz (Jan, son of Dirck Jansz). The other solution to get a better distinction between people was the use of family names. These family names didn't come into use everywhere at the same time. First they emerged in the towns and later in the smaller villages. Now in the villages under concern here (Wormerveer, Krommeniedijk) family names were almost completely unknown until the beginning of the 17th century. After that they came into use within a relatively short time and almost all people had such a family name by the end of the 17th century. In other parts of the country this development went much slower. For instance, in the provinces of Groningen and Drenthe, so the region where the other Dutch Aten-family originates from, a majority didn't have any family name until 1813, the year it was ordered by law that everybody had to have one.
In the 17th and 18th century everyone was free to choose his or her family name. This means, that a son could use the family name of his father, but was also free to choose a new one. So there are lots of examples of a father with several sons, all of them using different family names! Also it was quite normal for one person to have several family names. It was not before 1813 that this praxis was prohibited. Why do I tell you all this? To be able to explain why a son of Trijntje Dircks Aten used the family name Aten. In those days, children were named after some relative. The normal rule was (and still is in some families): the first son was named after the fathers father, the second son was named after the mothers father, the first daughter was named after the mothers mother and the second daughter was named after the fathers mother. From the third son or daughter onward there weren't any strict rules, but mostly the children were then named after an aunt or uncle. However, if an aunt or uncle had died already at a young age, their names were often preferred even before the names of the grandparents. And especially in our villages, but elsewhere also, there was a peculiar praxis of not only giving a relative's first name but also his family name to a new born child!
I'm sure this IS complicated! When you read it several times I hope it will become clearer. But the next case gives a good illustration of all this and you'll understand I couldn't avoid telling it.
We just have a look at the children of Cornelis Dircksz Moolenaer also known as Mots and (I didn't tell you before) also known as De Boer. Here we have such a person, having three family names! He married Trijntje Dircks Aten. The first son was named after his fathers brother Jan, because this uncle already died young and the son therefore was called Jan Cornelisz. Because this Jan Cornelisz also died young he wasn't found with a family name in the sources. The second son was named after the fathers father Dirck and was therefore called Dirck Cornelisz. This Dirck Cornelisz probably didn't like any of all his fathers family names, because he chose to call himself Dirck Cornelisz Blank. Then the third son could have been named after his mothers father but his parents preferred another young died uncle, the mothers brother Willem. And here they did not only give their child the first name Willem but also the last name Aten, so this third son was called Willem Cornelisz Aten! So: yes indeed, one son became to carry the mothers (but actually more precisely his uncles) maiden name!
I hope that my limited abilities to express myself in English will not prevent you from studying this indeed complicated matter. If you are even more puzzled now than you were before, just ask again and I will give another try.
About the years: I intended to use symbols that are common in genealogy but apparently they are common only in Europe. A "+" should express: "died", a "*" should express "born". It all fits then.
What the connection of AHA to the Krommeniedijk Aten line concerns: I'm very much aware of the corresponding first name that turns up here. I saw in the Proceedings of the New Jersey Historical Society, Notes on the Aten (Auten) family, page 236, where the signature of AHA is reproduced, that he himself wrote his name "Arien hendrickse(n) Aten" (the line downward after the "e" in hendrickse is the normal shortening for an "n" at the end of a word). But Aerian, Ariaen, Arien or Arie are all very normal variations of the name Adriaen (or in modern spelling Adriaan). And although this name wasn't in the top ten of most frequently used first names, it was quite common then as it is nowadays. We should however exchange detailed arguments why or why not he could be a relative, this being a topic for some of the next mails. But the first important argument I do want to give already: all the above Atens in Krommeniedijk and Wormerveer were Mennonites, which makes it unlikely for them to have had Reformed relatives, since marriages between these two groups were strongly condemned. But don't get me wrong. As long as we don't know the truth about AHA I can't rule out any possibility. But we can get closer to a solution when we study probabilities.
You're question about the Dutch pronunciation of Aten is really difficult to answer merely by writing. The Dutch "a" sounds different from anything you have. It sounds a bit like "a" in "father" and you can try to make a Dutch "a" if you speak the word "father" loudly with an exaggerated wide and broad opened mouth. This should sound totally different from the spelling variations that developed in America like Auten or Eatan or Ayten. Just try! Tell me if it works!