Hi Kevin..I dont think that there is any connection..going on the traditionanl way of naming Irish males..1st Son after Fathers Father..I have not come accross any Patrick's in our family.. have you tried your searches using the many variants, O'Halloran/O'Holleran/Holloran/Halloran as even up to the mid 1900's different members of my own family circle where using differnt spellings..if anything does come my way I will let you know...there seems to be a strong Patrick naming of Hollerans in the Ballina region of County Mayo.
Good Luck in your searche's.
Frank