Those with no romance in their souls assert that the place-name Dundee comes from a Gaelic original meaning something like ‘excellent hill’, which is plausible enough and might even be true. A more romantic explanation if given in some sources, connecting the city’s name with the prince who elevated it to the status of a burgh. David, the Earl of Huntingdon and brother of King William the Lion is supposed to have participated in the Third Crusade of 1189-92. He was shipwrecked off Egypt, but was saved by a slaver and sold on to a rich Venetian. Luckily for him, an English merchant recognised Earl David and he was set free. But journeying back to Scotland, his ship nearly sunk during a ferocious gale in the North Sea. So David got down on his knees and prayed to the Virgin Mary to save him, promising to build a kirk in her honour in the place where he came to land. As the clouds momentarily parted he caught a glimpse of a hill and told the crew to steer towards it the mount. The hill was of course Dundee Law and the ship landed nearby on the north shore of the River Tay. In thanksgiving, David named the place Deidonum, the ‘Hill, or Gift, of God’. He later built his promised church, which came to be known as the Kirk in the Field, where his daughter Margaret married Alan, Lord of Galloway, in 1209. The whole legend has the same flavour of the tale attached to King Alexander I, who was case ashore on Inchcolm in the Firth of Forth and founded a religious house there.
But another theory connects Dundee’s name with the Old Irish word daig, which was both a noun meaning fire and a personal name. The summit of Dundee Law had a vitrified fort, with timber walls deliberately fused together with fire, and so Dun Daig, the ‘fort of fire’, seems an appropriate explanation of the place-name. One legendary figure named Daig was the son of an Irish exile named Corc who came to Angus perhaps in the 4th century. Corc himself was the son of King Lughaidh, King of Munster, who banished him to Alba. In this foreign land, Corc almost perished in a blizzard, but he was saved by the bard of the local Pictish king. The bard also noticed a magical message written on Corcc’s shield at the behest of his father. The message directed the king of Pictland to kill Corc. But the poet changed the words to request the king to give Corc every assistance he could and even give his daughter to the Irish immigrant, which is exactly what happened. Prince Corcc remained in Pictland until he had seven sons and an immense fortune. Apart from his son Daig he had another who founded the Eoganacht kin-group of Circinn, and was possibly the ancestor of the Pictish king Angus mac Fergus.
So, we have three versions of the origin of the name of Dundee, and as non can be definitively proven to be correct, you can choose which one you prefer. I know which one I believe.