Both names are perfectly acceptable in use today - The BAC one being the official name - but I can't say as to why.

Dubh linn - later anglicised to Dublin (easier to pronounce) is the older name refering to the place where the city later grew around, But BAC refers to the Town of the ford of the hurdles... so one is a spot the other a town... sounds a good theory for a pub discussion anyhow.

If anybody is seriously interested though - and has serious hours to spend reading (I'll leave the pronunciations to yourselves) check out the link below for Dublin history ....seriously good site

Diesel

http://indigo.ie/~kfinlay/