Hello, just noticed your posting from 3 months ago and thought I should reply. I am not an expert on the Kavanagh name in NL, but have researched the name as it exists in my family tree.
The short answer to your question is yes the Kavavnagh name exists in NL and it is not an uncommon name. My Kavaangah ancestors arrived before 1821 from Ross Parish, County Wexford and the Kavanagh name was here before then and very much exists today. I have seen it spelled Kavanagh/Cavanaugh/Kavana and likely other variations.
I have not researched the Kavanagh name after the 1890’s as my Great Great grandmother Ellen Kavanagh married and we “lost” the name.
You may have some success if you know the religion and location of your uncle, as a place to start. Mu ancestors were Catholics in St. John’s but I have seen the name in several locations/communities throughout the province; Bell Island, The Southern Shore and perhaps others.
The records before the 1920’s are more accessible than those after the 1920’s.
Hope this helps