The marks left by argon do not impair the liver's function and disappear by themselves. The offences relate to the incidents on 9 February and 21 August 2013.
Bramhall pleaded guilty in December to two counts of assault by beating after pleading not guilty to assault occasioning actual bodily harm.
Bramhall, of Redditch, Worcs, worked at Queen Elizabeth Hospital in Birmingham for 12 years before he quit.
Cell phone pictures were taken of the branding, and Bramhall later admitted to the act.
Bramhall tendered his resignation the following summer amid an internal disciplinary investigation into his conduct. However, it failed a week later - for reasons unconnected to its implantation - and another surgeon noticed the initials then, the court heard. He's now employed in Herefordshire, at NHS.
He said the victim who had been identified in the "unique" case had suffered minor physical injury and psychological harm.
But the surgeon used the device to burn his initials "SB" into the livers of two patients.
Defence barrister Michael Duck QC said: "A number of people who sit in this court are able to sit in this court because of the skill of Mr Bramhall".
A nurse who saw the initialling queried what had happened and Bramhall was said to have replied: "I do this".
Crown Prosecution Service Head of Special Crime Frank Ferguson said Bramhall was a very respected surgeon and that many patients owed their lives to him, the Birmingham Mail reported.
Medical experts have said that the "burning" of organs would not have caused damage to their health or affected clinicial outcomes for patients.
Bramhall arrived at court for sentencing today (12 January) and was also handed a 12-month community order.
"Both of the operations were long and hard".
"I accept that on both occasions you were exhausted and stressed and I accept that this may have affected your judgment", the judge continued.
Bramhall claimed he had been "tired" during the surgeries, but Judge Paul Farrer said he had shown "professional arrogance of such magnitude that it strayed into criminal behaviour", according to media.
The judge said that what Bramhall did was a betrayal of his patients' trust. "I accept that you didn't intend or foresee anything but the most trivial of harm would be caused".
Tony Badenoch, prosecuting, said the freaky incidents took place at Birmingham's Queen Elizabeth Hospital in 2013.