The Irish Times website has the following to say about the surname Salmon in Ireland and it's frequency between 1847-64 (the time of Griffiths Primary Valuation).
numerous (239 households) : all areas, especially Mayo-Galway, Down. Ir. Ó Bradáin, bradán, a salmon. East of the Shannon, it is likely to be English.
I have also heard that Salmon is sometimes a Jewish surname, possibly a corruption of Salomon or Zalman.
Justin