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The glacier was discovered by the Second German Antarctic Expedition, 1911–12, under Wilhelm Filchner, who named this feature for Count Hugo von und zu Lerchenfeld-Köfering, a supporter of the expedition.
Surveyed by the SGS in the period 1951-57, and named by the United Kingdom Antarctic Place-Names Committee (UK-APC) for Johannes Muller, Second Officer and navigator of the Deutschland during the German Antarctic Expedition, 1911-12.