Most irish names you need to be looking for alternate spellings, some far more diverse than Gleeson/Gleason. Names were spelled as sounded to the writer of passenger lists.
The earlier they are the most diverse due to many people not being able to read and write. Even in the 1901/1911 many people still did not read or write.Often spellings of names changed on immigrating as well and spelled by the ear of
the writer. My husband's family were Codd's in Ireland and
Code/Coad in Canada, Cody in the USA.
The Griffith Valuation of 1846-1875 depending on the county
and as you are on Tipperary message board, there were
1,023 Gleeson's in just the North Riding of Tipperary 1852 and
154 Gleeson's in the South Riding of Tipperary 1850.
(helpful if you have parish)
(simpler version by Parish & Townland then can go to the 1st.source