The name "Marduk", as in the deity, was originally written 𒀭𒀫𒌓. This spells out something like amar utu, with the first sign being silent (
[D] for short—basically meaning "what follows is a divine name", for disambiguation). All together, it means something like "solar calf", in Sumerian.
When the Akkadians and others borrowed the writing system, though, they didn't always use it phonetically. When they wanted to write about Marduk, they used these same signs for Marduk—even though the Akkadians pronounced their deity's name Marduk, and the signs phonetically spell out Amar Utu.
This is called a Sumerogram, and in Latin transcriptions, it's written with capital letters to show that those letters have no relationship to the actual pronunciation. When an Akkadian-speaker writes 𒀭𒀫𒌓, we transcribe it as
[D]AMAR.UTU, and it phonetically spells out amar utu, but the actual intended pronunciation was more like marduk.
So the capitalization in the British Museum's transcription is important: Marduk-nadin-ahhe's name, as written on the blade, is
[D]AMAR.UTU-SUM-ŠEŠ.MEŠ. In other words, there are three different Sumerograms, which represent Sumerian words pronounced amar utu, sum, and šeš meš.
But the name, as actually spoken, used translations of those three words: Marduk, nādin, aḫḫē. That is, his name was pronounced something like Marduk-nādin-aḫḫē by his subjects, despite the spelling—amar utu sum šeš meš is just what you get when you read the characters as if they were Sumerian.
(His name is also sometimes written as
[M][D]AMAR.UTU-na-din-MU, using a mixture of Sumerograms and actual phonetic characters. Here, the characters in the middle actually represent the pronunciations na and din, not any meaning in Sumerian.)