Stoutenburgh and all its variants (Van Stoutenburg, Stoutenberg, Stoltenberg, Stolzenberg) derive back from the castle Stoutenburg near Amersfoort. Although it wasn't finished, Wouter van Amersfoort already gave it to the Bishop of Utrecht (Hendrik van Vianden). This happened on the 12th of June in the year 1259, the same day on which the city Amersfoort got its city rights from also Bishop Hendrik van Vianden. As the family Van Amersfoort was a very important family hailing from Amersfoort, this all smells like a sort of deal between Wouter van Amersfoort and the Bishop. The castle doesn't exist anymore, but at its place there can be found a house (a big house, that is).
The meaning of the name Stoutenburg falls apart in two: stout and burg . The latter has the meaning of 'fortress', like the nowadays Dutch word burcht . The first component nowadays has the meaning of 'bad, naughty', but the Dutch word stoutmoedig ( moedig means 'brave') shows us an altered meaning. In fact, etymologically there is a connection with the German word stolz , which means 'proud'. The Dutch stout used to mean something like 'proud' as well (or 'self-assured'). This meaning is the same in the Dutch surname De Stoute , which refers to a characteristic of the first bearer.
important: stout didn't mean 'brave', like Anon. said. And stoutmoedig means 'very brave'.