Why do you think its definitely a surname?
I have come across Jarvis variant Jervis as a surname in the past.
When I said 'definitely a surname' it's likely anyone with Jervis as a forename/middle name has inherited it from the surname.
An e.g. 'Macaulay Culkin', Macaulay is more prominent as a surname than a forename.
A few searches on the name Jervis forename & surname & by far the name is more often used as a surname &/or a middle name rather than a forename.
When surnames are used as middle names it's usually an indication of a relationship/connection with that surname, often from the maternal line although not always.
Where there's illegitimacy, a surname as a middle name is often an indicator of the father again not always.
if there is an Irish connection, could you give me some clue where I should start looking??
The suggestion is only a possibility with the 'combined' names.
I wouldn't be looking in Ireland but closer to home.
I haven't read through all your threads but I would begin with finding out whether the names Desmond &/or Jervis have been used earlier on the maternal lines.
If not, I would be looking in the area where your ancestor was born, on census records for those names & Jervis whether surname or forename as a start.
Hope this helps to answer your questions?
Annie