Dwyer - Hannon/Hannan Family

I have reached a roadblock finding any information prior to 1860 for Michael Dwyer amd Mary Hannon. We believe they were both born around 1815. They had a son Patrick born around 1839.  Mary and Patrick came to the US in 1860 or 1861. I haven’t found any record of Michale coming. My father seems to recall his father telling him they came from Tipperary but I’ve found Patrick’s obituary which says he was born in Limerick. I’m not sure if that means the town or county so I thought I would start here. I know that back then there was a particular naming convention of children (eg eldest son named for fathers father, second eldest for mothers father, etc). It seems Patrick and his wife Sarah (married in the US) followed the traditional naming convention with all their  children - both daughters and sons except the first born son. Patrick’s first born son was named Bartholomew...I would have expected it to be Michael. This tells me maybe there was another son born first named Michael but he died but that wouldn’t make sense because then Bartholomew would have been named Thomas after the mothers side. So my next thought is that we are incorrect about Mary’s husband being Michael Dwyer...maybe it was Bartholomew? Or maybe Michael is his middle name. Anyway, a lot of rambling but it’s all Ihave to go on. Any insight would be helpful or suggestions on where to search for info. Thank you Donna