I asked my Bosnian colleagues how this had come about, but they professed ignorance, other than confirming that "Irac" does indeed mean "Irishman", and so I left the issue as one of many intriguing mysteries about the country.
Well, I have come a little closer to resolving it. The street name next to the place name on the map is "Ivana Markovića Irca", and a little digging leads me to a Serbian Wikipedia page about Ivan Marković "Irac", a Partisan fighter during the second world war - Tuzla was always proud of its Partisan tradition, and Marković was a local boy from Gračanica, northwest of Tuzla - and was eventually hunted down by the Chetniks in 1942 a few km to the east of the city, so obviously the glorious people's planners of a later decade decided to commemorate him. There appears to be a school (maybe two schools, I'm not sure) named after him in Špionica farther to the north.
The Wikipedia page does not, however, explain how he got his nickname, and I remain puzzled. Just for context, I note that he was a Bosnian Croat. It is not easy to dig into this when my command of the language is rather basic and when there are lots of other people with the same or similar names - such as for instance the Slovak intellectual Ivan Markovič who died in Buchenwald two years after his near namesake was killed on the Bosnian mountainside. So the mystery, though now slightly enriched, remains.