I was thinking more of the Tudor attempted anglicisation of Ireland - esp around the 1570-1600 but a quick look at my history books doesnt show any specific attampt to outlaw Irish names. (there was an outlawing of Welsh around this period - possibly there names were foreably anglicised)
However during the Elizabthan conquest of Ireland the Island kept quiet (though it does appear that the English avoided using the Island even though Elizabeth had assumed control during the disputed Stanley succession) - the English (or rather better I think Lancashire) colonization did not, it appears raise a rebellion until Earl James attempted to impose significant changes in land holding - this lead to the rebellions in 1640's and 50's. It may well be that the Mac's were dropped as part of the anglicisation of the Island which had been going on for about 200 years by the time most surviving Parish registers date from. It may well be that the overwhelming success of the campaign in Ireland demonstrated that it was probably better to align oneself with the English