Depending on the part of the Netherlands he was from, there would be a wide variety of reasons a man would go by his mother's name or name his children his mother's last name. Many of my ancestors and their relatives in Noord-Holland did so because of money, or to keep a name from dying out, or to distinguish between relatives who had the same first and last names, or simply because they decided it was a good idea. Some took their mother's father's first name and added "son" to it, for example Otzen for grandfather Otte.
However, I see that Jan Brouwer / Beugeling was from the province of Drenthe. It was very common for people to change their last names in Groningen, Drenthe, Overijssel and just over the Dutch border in Grafschaft Bentheim because of where they lived - at least, if they lived in a hamlet or out in the country. I have several ancestors from these areas who, when they left their parents' erve (manor or property), changed their last names. Last names often came with the property one lived on or owned. For example I have one ancestor, Harmen Veeneman, who did not inherit his father's property in Overijssel. He married Fenne Meijeringe who was a part owner of the Meijeringe property by Emmen, Drenthe. However, they lived in the erve called Klore in Grafschaft Bentheim that Fenne inherited from her father's mother. They are therefore found under 3 last names in various records (6 if you consider the Dutch and German variations to be different names): Veeneman / Fenmans, Meijeringe / Meijerink / Meyering / and Kleurs / Klore. When their youngest daughter married they gave her the Klore erve and she and her children took on the last name Klore. At the same time Fenne sold her share of the Meijeringe erve to a relative. Harmen and Fenne then moved to a city in Overijssel and Harmen kept the last name Veeneman.