The people who put up headstones have many names.
Stonemason, stonecutter, lettercarver, sculptor, and monumental sculptor are a few that come to mind.
Sometimes, about 1% of the time, we find the stonecutters name carved on the bottom of the headstone. It'll say something like Fecit D McCarthy.
Which is latin for D McCarthy made this!
The best book on Irish headstones is Mary Timoney's Had Me Made and she traces the history of monumental sculptors across County Sligo. But that is a rare piece of work. We know very little about these craftsmen in Ireland.
If you think your ancestor may have worked with stone; may have been a stonemason; or a monumental sculptor then once again, the http://census.nationalarchives.ie/ is an excellent tool for searching for them, because you can search the census by occupation.
Here's a quick video on how to search the census by occupation.
Step 0 - goto the website
Step 1 - click on Search
Step 2 - Select your year
Step 3 - click on More Search Options
Step 4 - enter occupation in the Occupation field
Step 5 - set results list view to greater than the default 25 and examine your list.