Daphne:
The subscription site Roots Ireland has a October 8 1854 baptism for a Bernard Clarke with father James and mother Pebby Clarke. The Drung parish register is not online at the NLI site so we can't check the name Pebby. Since his son was named James, it is possible he named the child after his father.
In any event, this is a lead for your research. DNA testing may be helpful also.
Roger McDonnell