The version you give (d Gish-gim-mash) is the spelling of the name in the first millennium BC 'standard version' of the epic, yes (in Babylonian = Akkadian language).

There are lots of variant spellings over c. 2000 years of transmission, and in the older Sumerian poems, the hero is called Bilgames. So there isn't necessarily a 'correct' way of spelling the name, but this is pretty much as close as you can get.

On the name and spelling variants, see George, The Babylonian Gilgamesh Epic, vol. 1, pp. 71-90