The Irish Roll of Honour has a Peter Culligan 29388 of Royal Dublin Fusiliers who was presumed killed on August 16th 1917, born Loughdavin, County Cavan
The Army Register of soldiers effects has this Peter Culligan too with effects going to a brother Owen, and sister Kate Kearney.
This Peter Culligan of the Royal Dublin Fusiliers attested in Greenock. It would appear likely therefore that the man on the Inverkip War Memorial is this Peter Culligan.
His name was spelled Colligan on the Inverkip War Memorial. This has now been corrected to Culligan. The spelling of names was often more to do with the person writing down what they heard rather than the family themselves. There are many cases of the same family spelling their surnames in several ways - especially Irish