The marks left by argon do not impair the liver's function and disappear by themselves.
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.
Bramhall resigned from his position at the hospital in the summer of 2014, while the investigation was still ongoing, but he was still allowed to practice. A photograph of the 4cm-high branding was taken on a mobile phone.
The woman, who said she didn't even like the ideas of tattoos on skin, told the court: "The horror of seeing the photo of my cut open body with the initials SB on the liver will forever live in my mind".
Last month, Bramhall pleaded guilty to two counts of assault by beating, after prosecutors accepted his not guilty pleas to charges of assault occasioning actual bodily harm relating to two patients.
The court heard that a surgeon colleague was "taken aback" when he discovered the initials SB on the patient's liver when removing it after it failed.
Birmingham Crown Court was told one of the victims suffered serious psychological harm as a result of the branding, while the other was traced through hospital records but "did not wish to engage" with police.
Bramhall now has to pay a £10,000 ($13,600) fine and perform 120 hours of unpaid work to make amends for his actions.
Bramhall's actions came to light when one of the patients had further surgery a week later.
Judge Paul Farrer QC, presiding over the case, reckoned that both liver transplant operations were hard and long, which likely made the surgeon stressed and exhausted, clouding his judgement.
"It was important to bring this prosecution, both for the victims and also to maintain the confidence of patients who put their complete trust in surgeons", said Frank Ferguson, head of special crime for the Crown Prosecution Service.
He told him: "I accept that on both occasions you were exhausted and stressed and I accept that this may have affected your judgement".
Birmingham's Queen Elizabeth Hospital issued a statement yesterday saying: "The Trust is clear that Mr Bramhall made a mistake and this has been dealt with via the appropriate authorities, including the Trust as his then employer".
Bramhal is due to be sentenced by Judge Paul Farrer QC on Friday morning.
"He knew that the action could cause no harm to the patient", said Mr Badenoch. "We can reassure his patients that there was no impact whatsoever on the quality of his clinical outcomes".