The Crown Prosecution Service (CPS) said Bramhall marked his initials on the patients' livers without their consent "for no clinical reason" using a medical instrument created to seal bleeding blood vessels.
Bramhall, of Tarrington in Herefordshire, was ordered to complete 120 hours of community service and pay £1,500 in prosecution costs.
The court heard Simon Bramhall was "extremely sorry" and wanted to apologise to the patient.
Bramhall resigned from the Birmingham hospital in 2014 after another surgeon found "SB" branded into a liver and raised concerns.
The consultant, who was given a formal warning by the General Medical Council (GMC) last February, admitted two counts of assault by beating last month after prosecutors accepted his not guilty pleas to charges of assault occasioning actual bodily harm.
The liver was salvaged from the plane and Bramhall successfully transplanted the liver into the patient and saved the patients life.
Opening the facts of the case against Bramhall, Tony Badenoch QC, prosecuting, said one of the surgeon's victims had been left feeling "violated" and suffering psychological harm.
Defense attorneys argued Bramhall's acts were a "naïve and foolhardy" attempt on his part to relieve the tension of multiple operations, the BBC reported.
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The president added that the US government should accept more people from countries like Norway . Graham's statement did not detail what Trump said or what Graham told the president in response.
Simon Bramhall was a respected surgeon known for his meticulous work in the operating theatre.
It was only when one of the livers failed - for reasons unconnected to Bramhall's actions - another surgeon discovered "SB" burnt onto it and took a photo of the 4cm mark.
"It's applying the current law to a unique set of circumstances, so in that sense it's a precedent because we've never come across a situation where a battery has taken place in these circumstances but the criminal law applies to everyone". It leaves surgeons facing further scrutiny legally - not just over medical mistakes for which they might be sued - but over what some might have regarded in the past as harmless medical pranks.
The General Medical Council said past year that Bramhall's conduct risked bringing his profession into disrepute and issued a warning to him but did not think it warranted further punishment.
Mr Badenoch said: "This case is about his practice on two occasions, without the consent of the patient and for no clinical reason whatever, to burn his initials on to the surface of a newly-transplanted liver".
A nurse asked what the marks were and Bramhall was said to have replied: "I do this".
Sentencing Judge Paul Farrer QC said the assaults had been born out of 'professional arrogance'. I accept that on both occasions you were exhausted and stressed and I accept that this may have affected your judgment.