The fjord is named after the Dutch whaler Willem Cornelisz. van Muyden, who was involved in the trade in 1612 and 1613. Van Mijenfjorden (an obvious corruption of Van Muyden's name) was originally called Low Sound, while the small cove north of Axel Island (at the mouth of the fjord) was called Van Muyden's Haven. This latter name was moved from its proper location by Giles and Rep (c. 1710) and "floated over" to where modern cartographers now wrongly place it.
Conway, W. M. 1906. No Man’s Land: A History of Spitsbergen from Its Discovery in 1596 to the Beginning of the Scientific Exploration of the Country. Cambridge: At the University Press.