Did some reading on this last night. These are probably not definitive answers but the books said as follows :

Ath Cliath (ford of the hurdles (or wattles)) is actually (according to one book at least) a more ancient name than Dubh Linn. The ford in question formed part of one of the five main roads in ancient Ireland which radiated out from Tara in county Meath, which was in effect the ancient capital of Ireland and seat of the high kings. There does not appear to have been a big settlement there at the time, but the ford being part of such a major road - leading to what is now Dublin Bay, would probably be well known throughout Ireland.

Incidentally the ford is thought to have been where the current Father Mathew bridge at Church St now stands. This is adjacent to the Brazen Head, reputed to be the oldest Pub in Dublin dating from 12th Century. This was once a great place for traditional music and is still a music venue.

The name Dubh Linn also goes way back and it is thought that Eblana, referred to by Ptolemy in 3rd century AD, is derived from this name. Apparently the reference by Ptolemy was not to a city as such, but to an area inhabited by people he called the Eblani. This area (the pool was around the site of the current Olympia theatre in Dame St (and not that far from the ford)) was inhabited by the Norse in the Ninth Century, who called it Dyfflin - obviously another derivative - this (or the original name) became anglacised to Dublin over the years.

So the Gaels would probably always have referrred to the place as Ath Cliath, and the strangers called it Dublin, and so it remains. But I'm sure there are many other versions of the story.