LONDON — A prominent British surgeon who etched his initials onto the livers of two patients, in a case that shocked many with its audacity, has been convicted of assault.

The surgeon, Simon Bramhall, who gained fame in 2010 after successfully transplanting a plane-crash victim’s liver into a patient, pleaded guilty in Birmingham, England, on Thursday to two counts of assault by beating.

The case divided opinion in Britain. Many have expressed outrage, while others — including some former patients — have defended him.

According to British news reports, Mr. Bramhall, 53, admitted to using an argon beam — an electrified gas jet that liver surgeons typically employ to stanch bleeding or to mark an area of operation on an organ — to etch “SB,” his initials, onto the livers.