The Irish called their little community Atha Cliath, and the Vikings called their one, which was a little further downstream, Dyflin. They were neighbours.
Atha Cliath (Hurdle Ford) was located at a shallow point of the Liffey, caused somewhat by Usher's Island. Usher's Island has now been built up and is part of the South Quay a little east of the Guinness Brewery, it no longer is an island, but it is still known as Usher's Island with Island Road paralleling the river. The ford went across the Liffey just after the island up to the far side, just East of were Collins Barracks is now.
Dyflin was located just East/SouthEast of the Black Pool, caused by the River Poddle. That goes more or less under the Temple Bar area, it's a notable dip in the road going West from College Green towards ChristChurch. Not that the Poddle was a major waterway, but it very clearly was a delineation between the areas of the Viking and the Irish settlements.
Eventually the two towns merged into one city. The Irish kept calling it by their historical name of Baile Atha Cliath (Town of the Hurdle Ford), and the Vikings and later Anglos kept calling it their name of Dubh Linn (Black Pool).