"...his father’s rank or profession simply says “esquire”"
What was put down as the father's profession generally depended on what the person getting married actually told the vicar. A person could say that their father was whoever they said.
So job descriptions aren't always entirely accurate - it was what the child perceived their father's profession to be.
Where a particular 'profession' wasn't given then a 'rank' would be given. This was often 'gentleman' or 'esquire'.
Basically, this meant that the person had private means - they didn't have a job. For example, he may have been somebody who owned a country estate or he may have had an inheritance invested in government bonds that paid out an annuity.
For example, the novel Pride and Prejudice was published about 25 years before this and Mr Bennet (the father of Jane and Elizabeth and the others) would likely have been described as 'gentleman' or 'esquire' at the time.
However, some barristers (who worked for a living) were also referred to as 'esquire'.
The easiest step would be to look for the father in the 1841 census. This will likely give a better indication of his status.
.
"His father’s name is listed (different surname which is interesting)"
If he has a different surname to his father then one possibility is that he was illegitimate (ie his parents weren't married) and that he was baptised with his mother's surname.
.
"I’ve reached a bit of a dead end and am pretty clueless.
can anyone please fill me in? Thanks!"
If you like I can have a look to see what records are available. If you want to send me a DM with whatever information you feel happy sharing then I can have a look at Ancestry and FindMyPast to see what information is available there.