Bergh's full names were Ludvig Sophus Rudolph, but all his publications appeared under the name Rudolph Bergh. He was a Danish physician and malacologist and should not be confused with his son, the Danish zoologist and composer Rudolph Sophus Bergh (1859-1924). Bergh senior received his medical degree in 1849, worked for most of his career in hospitals in Copenhagen (one of which was later named after him), and became an authority on sexually transmitted diseases. As a malacologist he published many articles, reports and monographs (in Danish, German and English), most of which dealt with the Opistobranchia (a sub-class of gasteropod molluscs, including the sea hares and nudibranchs), and more specifically with the nudibranchs (shell-less marine gasteropods), on which he became a leading expert. In 1870 he described the nudibranchs of Mauritius and other places, in K. Semper's account of travels in the Philippine Islands. In 1884 he published an account of the nudibranchs dredged by HMS Challenger during its expedition of 1873-1876. In 1892 he described the Opistobranchia collected on expeditions by Prince Albert I of Monaco in his yacht l'Hirondelle. In 1902 he described the Opistobranchia collected by the Danish expedition to Thailand during 1899-1900. And in 1905 he described the Opistobranchia collected by the Dutch Siboga expedition to Indonesia, in which he took part.
Bergh's contribution to southern African science consists of an extensive review, "The Opisthobranchiata of South Africa", which was published as a contribution to Marine investigations in South Africa (1908, Vol. 5, pp. 1-144). This volume was also issued as Volume 17 of the Transactions of the Philosophical Society of South Africa (1907-1908). The South African marine mollusc Philine berghi was named after him, as was the nudibranch genus Berghia.