It seems commonplace for characters within the world of Final Fantasy XII to use aliases and pseudonyms at one point or another in the game. Although in the case of Ashe and Larsa, the use of an alias is for their own protection due to these characters’ political influences and their delicate social standings. For Gabranth, his choice of how he addresses himself is both political and personal.
According to the Final Fantasy XII Scenario Ultimania, it is a common practice amongst the Judge Magisters to address themselves using their own surnames.2 This practice seems to hold true for Gabranth as well, however, the name he has chosen for himself is not his own surname but his mother's maiden name.
As revealed by Basch after the party fought with Gabranth on the Bahamut, Gabranth's birth name is Noah fon Ronsenberg. When Basch called Gabranth by the name of Noah at that very moment, Gabranth told Basch that he had no rights to be called by that name, hinting at the possible reasons why he chose to be called Gabranth as a Judge under the Archadian Empire.
Although not fully explored within the context of the game, the Scenario Ultimania mentioned that after Landis, the homeland of both Basch and Gabranth, fell into the hands of the Archadian Empire, Basch fled to Dalmasca, while Gabranth was left with his sick mother and ultimately chose to relocate to Archades, his mother's birthplace.3
When Gabranth and his mother first arrived at Archades, their social standings were equivalent to those found in modern-day Old Archades – the lowest social class possible within the Imperial City. Perhaps it was to support his mother and himself or even a plot to eventually seek revenge for his fallen homeland, Gabranth threw away the name Noah fon Ronsenberg while he climbed the social ladder with his own abilities, stifled his resentment towards the Empire and sucked up to people of influence in order to rise to the rank of Judge Magister. During his ascend on the social ladder, Gabranth was unable to bid his final farewell to his mother as she passed away, alone, without anyone by her deathbed.4
For Gabranth, the name Noah represents his past and his associations with his homeland of Landis, before it was conquered by the Archadian Empire. His tremendous guilt – of not being able to defend his homeland, of having to seek refuge from and eventually aiding his enemies, and of not being able to be by his mother’s side as she was dying, prevents him from feeling deserving of his original name. In his mind, his identity as Noah was destroyed as he left his homeland and re-established himself as Gabranth, Judge Magister under the Archadian Empire.