Thaddeus Sholto's brother's name is Bartholomew.
In Arthur Conan Doyle's The Sign of the Four, Bartholomew Sholto is presented as the brother to Thaddeus Sholto. Thaddeus is depicted as being more conscientious and proactive, particularly in sending the valuable pearls to Miss Morstan. Bartholomew's eventual death plays a significant role in the plot, leading to Thaddeus's understandable worry about being accused of murder.
