I am afraid the only information we know for certain about the man Stortebeker is his last name. The story of his capture and execution has been embellished with many details over the years, only some of which are at least connected to historical facts.
The only contemporary account I am aware of is Chronica novella by Hermann Korner (around 1365 - 1438) of Lübeck. This city in Northern Germany, on the shores of the Baltic Sea, is located about 65 km North East of Hamburg, and both Lübeck and Hamburg were leading cities of the Hanseatic League, a large medieval mercantile network of towns involved in long-distance trade. Korner prepared his original manuscript in 1416, but refined it multiple times over the subsequent decades. I consulted a transcription of the manuscript(s):
Jakob Schwalm (ed.), Die Chronica Novella des Hermann Korner. Göttingen: Vandenhoek & Ruprecht 1895.
On pp. 98-99 Korner reports this among the events of the year 1402:
Hamburgenses [cives] duplex navale bellum habuerunt cum pyratis [Rostoccensibus et Wismariensibus licet protunc essent ab eis licenciati]. Horum capi tanei et duces in primo conflictu fuerunt Wichmannus et Stortebeker. Et Hamburgenses ex eis interfecerunt 30 prope Hilghelant 70 vero secum ducentes in Hamborg decapi taverunt [et capita abscisa iuxta Albiam statuerunt]. In secunda vero reysa capitanei pyratarum fuerunt Gotfridus Michaelis et Wigboldus magister in artibus. Et capti sunt a Hamburgensium mercatoribus circiter 80 et omnes capitibus sunt truncati [et appositi aliis].
This says that the citizens of Hamburg fought two armed engagements with pirates from Rostock and Wismar. In the first of these the pirates were led by Wichmann and Stortebeker. The Hamburgians killed 30 of them near the island of Heligoland and took a further 70 with them to Hamburg, were they were beheaded and their heads staked along the river Elbe. In the second engagement, the captains of the pirates were Gotfrid Michael and Master Wigbold and the Hamburgians captured around 80 of them, all of whom they beheaded and placed alongside the others.
Note that no first name is recorded for Stortebeker here. It is interesting to note that Wigbold is described as magister in artibus which I understand to mean that he held an M.A. degree. Describing the pirates as being based in Rostock and Wismar tells us that these pirates were connected to the Victual Brothers. A Nicolaus Stortebeker recorded in the court records of Wismar for the year 1380 has been considered by some to be identical with the pirate of lore (my bolding):
Balhorst Boldelaghe et Craan eo (scil. ab juraverunt civitatem) quod Ghero servo Poppen et Nicolao Stortebeker cuilibet ossa fracturus cum V blaviis intulerunt tempore nocturno.
While both Rostock and Wismar are located on the Baltic Sea, the pirates were operating in the North Sea at the time of their capture. As the pirates were interfering with Hansa trade, the Hamburgians sent Friedeschiffe (literally: peace ships) after them. In later retellings of the Storetebeker story the lead ship of the Hamburgians is often identified as the "Bunte Kuh" (variegated cow), but pretty much the only thing we know for certain about this ship is that it existed in the relevant time frame and what it cost to build and maintain, because financial records for the year 1402 are preserved in the archives of the City of Hamburg (my bolding):
8 ℔ Symoni de Utrecht pro labore et destructione navalium instrumentorum, quando Godeke Michahelis et alii fuerunt capti.
6 ℔ 4 β eidem pro anchoris lanceis et expensis carpentariorum.
[...]
32 ℔ Hermanno Nyenkerken pro labore et navalibus destructis ad usus navis buntenko dicte.
[...]
24 ℔ Wernero de Ulsen pro eo, quod ceperunt Godeken Michahel et suos complices
The Godeke Michahel mentioned in the financial records is the same person as Gotfrid Michael in Korner's account. While both were written in Latin, the Hamburgian records show names close to their original Low German form, while Korner fully Latinized them.
Ubbo Emmius was the first to attempt a comprehensive history of East Frisia: Rerum Frisicarum Historia, Leiden: Lodewijk Elzevir 1616. From what I understand he had access to many important primary written sources and is generally considered reliable. On pp. 225-226 he recounts the backstory of the pirates from Rostock and Wismar and reports that they raided as far as the important Hansa trading post of Bergen in Norway. He then states that the pirates used force to set themselves up in a winter shelter in East Frisia in 1396, and that the tom Brok family was among the first to befriend them there.
The chieftains of Brokmerland came from this powerful family. Embellished versions of the Stortebecker story usually identify the winter quarters as the town of Marienhafe, and some claim that Stortebecker married a daughter of the tom Brok family in 1396. I have read up on the tom Brok family and Marienhafe in proper history books (those that cite their sources) and could find no evidence of such a marriage, nor is it mentioned by Emmius.
